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## Journal of Knot Theory and its Ramifications

 Short Title: J. Knot Theory Ramifications Publisher: World Scientific, Singapore ISSN: 0218-2165; 1793-6527/e Online: https://www.worldscientific.com/loi/jktr Comments: Indexed cover-to-cover
 Documents Indexed: 2,451 Publications (since 1992) References Indexed: 2,107 Publications with 29,889 References.
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#### Latest Issues

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#### Authors

 62 Kauffman, Louis Hirsch 45 Manturov, Vassiliĭ Olegovich 31 Nelson, Sam 24 Lee, Sang Youl 23 Saito, Masahico 23 Silver, Daniel S. 22 Kawauchi, Akio 22 Lambropoulou, Sofia S. F. 22 Przytycki, Józef H. 21 Nakanishi, Yasutaka 21 Williams, Susan G. 20 Kanenobu, Taizo 19 Bae, Yongju 19 Diao, Yuanan 19 Ernst, Claus 19 Kamada, Seiichi 19 Ohyama, Yoshiyuki 18 Jin, Gyo Taek 17 Oh, Seungsang 16 Im, Young Ho 16 Jablan, Slavik Vlado 15 Hoste, Jim 15 Taniyama, Kouki 14 Adams, Colin C. 14 Carter, J. Scott 14 Hillman, Jonathan Arthur 14 Mellor, Blake 14 Ozawa, Makoto 14 Teragaito, Masakazu 13 Jeong, Myeong-Ju 13 Satoh, Shin 13 Shimizu, Ayaka 13 Traldi, Lorenzo 12 Cheng, Zhiyun 12 Lei, Fengchun 12 Yetter, David N. 11 Hayashi, Chuichiro 11 Jin, Xian’an 11 Kadokami, Teruhisa 11 Kamada, Naoko 11 Lee, Junghoon 11 Lopes, Pedro 11 Montesinos-Amilibia, José María 11 Nakamura, Takuji 11 Sazdanović, Radmila 10 Bardakov, Valeriĭ Georgievich 10 Dye, Heather Ann 10 Elhamdadi, Mohamed 10 Huh, Youngsik 10 Ito, Noboru 10 Lee, Sangyop 10 Morton, Hugh R. 10 Shanahan, Patrick D. 10 Tran, Anh Tuan 9 Fenn, Roger A. 9 Henrich, Allison K. 9 Horiuchi, Sumiko 9 Kim, Sera 9 Lee, Hwa Jeong 9 Miyazawa, Yasuyuki 9 Nikkuni, Ryo 9 Ogasa, Eiji 9 Yasuhara, Akira 8 Birman, Joan S. 8 Chmutov, Sergei V. 8 Chrisman, Micah Whitney 8 Frohman, Charles D. 8 Garoufalidis, Stavros 8 Hilden, Hugh Michael 8 Hsieh, Chun-Chung 8 Ichihara, Kazuhiro 8 Janse van Rensburg, Esaias J. 8 Kalfagianni, Efstratia 8 Kim, Jieon 8 Kim, Seongjeong 8 Lozano, María Teresa 8 Park, Chan-Young 8 Seo, Myoungsoo 8 Shibuya, Tetsuo 8 Stoimenow, Alexander 8 Takioka, Hideo 8 Tsukamoto, Tatsuya 8 Vesnin, Andrei Yu. 8 Yang, Zhiqing 7 Bar-Natan, Dror 7 Dabkowski, Mieczysław K. 7 Eudave-Muñoz, Mario 7 Fleming, Thomas R. 7 Foisy, Joel Stephen 7 Gordon, Cameron McA. 7 Ito, Tetsuya 7 Kim, Joonoh 7 Ko, Ki Hyoung 7 Kwon, Bo-Hyun 7 Lee, Kyeonghui 7 Millett, Kenneth C. 7 Mishra, Rama 7 Oshiro, Kanako 7 Tanaka, Toshifumi 7 Yashiro, Tsukasa ...and 1,800 more Authors
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#### Fields

 2,352 Manifolds and cell complexes (57-XX) 249 Group theory and generalizations (20-XX) 160 Combinatorics (05-XX) 85 Quantum theory (81-XX) 62 Algebraic topology (55-XX) 54 Differential geometry (53-XX) 51 Nonassociative rings and algebras (17-XX) 47 Associative rings and algebras (16-XX) 42 Category theory; homological algebra (18-XX) 38 Algebraic geometry (14-XX) 30 Biology and other natural sciences (92-XX) 28 Dynamical systems and ergodic theory (37-XX) 27 Global analysis, analysis on manifolds (58-XX) 24 General and overarching topics; collections (00-XX) 21 Number theory (11-XX) 19 Computer science (68-XX) 19 Statistical mechanics, structure of matter (82-XX) 15 Order, lattices, ordered algebraic structures (06-XX) 14 Probability theory and stochastic processes (60-XX) 13 Several complex variables and analytic spaces (32-XX) 12 History and biography (01-XX) 12 Convex and discrete geometry (52-XX) 11 Geometry (51-XX) 7 Mathematical logic and foundations (03-XX) 7 Commutative algebra (13-XX) 7 Functional analysis (46-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 General topology (54-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Topological groups, Lie groups (22-XX) 6 Real functions (26-XX) 6 Functions of a complex variable (30-XX) 5 Special functions (33-XX) 5 Relativity and gravitational theory (83-XX) 4 General algebraic systems (08-XX) 3 Approximations and expansions (41-XX) 3 Optics, electromagnetic theory (78-XX) 2 Field theory and polynomials (12-XX) 2 Measure and integration (28-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Numerical analysis (65-XX) 2 Mechanics of particles and systems (70-XX) 1 $$K$$-theory (19-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

1,717 Publications have been cited 9,467 times in 4,801 Documents Cited by Year
Racks and links in codimension two. Zbl 0787.57003
Fenn, Roger; Rourke, Colin
1992
Abstract link diagrams and virtual knots. Zbl 0997.57018
2000
Stable equivalence of knots on surfaces and virtual knot cobordisms. Zbl 1004.57007
Carter, J. Scott; Kamada, Seiichi; Saito, Masahico
2002
Temperley-Lieb algebras for non-planar statistical mechanics. – The partition algebra construction. Zbl 0804.16002
Martin, Paul
1994
On the invariants of torus knots derived from quantum groups. Zbl 0787.57006
Rosso, Marc; Jones, Vaughan
1993
Two-dimensional topological quantum field theories and Frobenius algebras. Zbl 0897.57015
Abrams, Lowell
1996
Geometric interpretations of quandle homology. Zbl 1002.57019
Carter, J. Scott; Kamada, Seiichi; Saito, Masahico
2001
Fast Khovanov homology computations. Zbl 1234.57013
Bar-Natan, Dror
2007
The skein method for three-manifold invariants. Zbl 0793.57003
Lickorish, W. B. R.
1993
Surfaces in $$R^ 4$$ of braid index three are ribbon. Zbl 0763.57013
1992
A sequence of degree one Vassiliev invariants for virtual knots. Zbl 1195.57030
Henrich, Allison
2010
Virtual crossing number and the arrow polynomial. Zbl 1195.57028
Dye, H. A.; Kauffman, Louis H.
2009
Perturbative Chern-Simons theory. Zbl 0861.57009
Bar-Natan, Dror
1995
Alexander groups and virtual links. Zbl 0997.57019
Silver, Daniel S.; Williams, Susan G.
2001
Link polynomials and a graphical calculus. Zbl 0795.57001
Kauffman, Louis H.; Vogel, Pierre
1992
Invariants of 3-manifolds derived from finite dimensional Hopf algebras. Zbl 0843.57007
Kauffman, Louis H.; Radford, David E.
1995
Categorifications of the colored Jones polynomial. Zbl 1083.57019
Khovanov, Mikhail
2005
Notions of positivity and the Ozsváth-Szabó concordance invariant. Zbl 1195.57029
Hedden, Matthew
2010
Unknotting virtual knots with Gauss diagram forbidden moves. Zbl 0997.57016
Nelson, Sam
2001
Virtual knot presentation of ribbon torus-knots. Zbl 0997.57037
Satoh, Shin
2000
Vassiliev homotopy string link invariants. Zbl 0878.57003
Bar-Natan, Dror
1995
State-sum invariants of 4-manifolds. Zbl 0883.57021
Crane, Louis; Kauffman, Louis H.; Yetter, David N.
1997
Extraspecial 2-groups and images of braid group representations. Zbl 1097.20034
Franko, Jennifer M.; Rowell, Eric C.; Wang, Zhenghan
2006
Invariants of colored links. Zbl 0758.57004
Akutsu, Yasuhiro; Deguchi, Tetsuo; Ohtsuki, Tomotada
1992
A formula for the A-polynomial of twist knots. Zbl 1057.57010
Hoste, Jim; Shanahan, Patrick D.
2004
On homology of virtual braids and Burau representation. Zbl 0997.57020
2001
Reidemeister moves for surface isotopies and their interpretation as moves to movies. Zbl 0808.57020
Carter, J. Scott; Saito, Masahico
1993
A note on non-classical virtual knots. Zbl 1094.57012
Kishino, Toshimasa; Satoh, Shin
2004
Rasmussen invariant, slice-Bennequin inequality, and sliceness of knots. Zbl 1148.57011
Shumakovitch, Alexander N.
2007
Forbidden moves unknot a virtual knot. Zbl 0997.57015
Kanenobu, Taizo
2001
Finite type invariants of integral homology 3-spheres. Zbl 0942.57009
1996
Idempotents of Hecke algebras of type $$A$$. Zbl 0924.57005
Aiston, A. K.; Morton, H. R.
1998
On the Casson knot invariant. Zbl 0997.57021
Polyak, Michael; Viro, Oleg
2001
Understanding the Kauffman bracket skein module. Zbl 0932.57015
Bullock, Doug; Frohman, Charles; Kania-Bartoszyńska, Joanna
1999
Colored HOMFLY polynomials from Chern-Simons theory. Zbl 1296.57015
2013
The $$(2,\infty)$$-skein module of lens spaces; a generalization of the Jones polynomial. Zbl 0796.57005
Hoste, Jim; Przytycki, Józef H.
1993
Distinguishing mutants by knot polynomials. Zbl 0866.57002
Morton, Hugh R.; Cromwell, Peter R.
1996
Virtual braids and the $$L$$-move. Zbl 1105.57002
Kauffman, Louis H.; Lambropoulou, Sofia
2006
Extensions of quandles and cocycle knot invariants. Zbl 1049.57008
Carter, J. Scott; Elhamdadi, Mohamed; Nikiforou, Marina Appiou; Saito, Masahico
2003
A multi-variable polynomial invariant for virtual knots and links. Zbl 1171.57006
Miyazawa, Yasuyuki
2008
Index polynomial invariant of virtual links. Zbl 1201.57005
Im, Young Ho; Lee, Kyeonghui; Lee, Sang Youl
2010
An affine index polynomial invariant of virtual knots. Zbl 1271.57040
Kauffman, Louis H.
2013
Minimal knotted polygons on the cubic lattice. Zbl 0797.57004
Diao, Yuanan
1993
Knot theory related to generalized and cyclotomic Hecke algebras of type $${\mathcal B}$$. Zbl 0933.57007
Lambropoulou, Sofia
1999
Magnetic graphs and an invariant for virtual links. Zbl 1116.57008
Miyazawa, Yasuyuki
2006
Invariants of knot diagrams and relations among Reidemeister moves. Zbl 0998.57021
Östlund, Olof-Petter
2001
Quaternionic invariants of virtual knots and links. Zbl 1149.57301
Bartholomew, Andrew; Fenn, Roger
2008
A polynomial invariant of virtual links. Zbl 1284.57005
Cheng, Zhiyun; Gao, Hongzhu
2013
Enumeration of chord diagrams and an upper bound for Vassiliev invariants. Zbl 0892.57003
Stoimenow, A.
1998
Generalized spin models. Zbl 0842.57010
Kawagoe, Kenichi; Munemasa, Akihiro; Watatani, Yasuo
1994
Remarks on the $$A$$-polynomial of a knot. Zbl 0890.57012
Cooper, D.; Long, D. D.
1996
Generalized Temperley-Lieb algebras and decorated tangles. Zbl 0926.20005
Green, R. M.
1998
On a calculus for 2-knots and surfaces in 4-space. Zbl 1001.57044
Swenton, Frank J.
2001
Stick numbers and composition of knots and links. Zbl 0884.57005
Adams, Colin C.; Brennan, Bevin M.; Greilsheimer, Deborah L.; Woo, Alexander K.
1997
Polygon indices and superbridge indices of torus knots and links. Zbl 0881.57002
Jin, Gyo Taek
1997
On the arithmetic 2-bridge knots and link orbifolds and a new knot invariant. Zbl 0844.57006
Hilden, Hugh M.; Lozano, Maria Teresa; Montesinos-Amilibia, Jose Maria
1995
Detecting non-triviality of virtual links. Zbl 1049.57006
2003
Introduction to virtual knot theory. Zbl 1255.57005
Kauffman, Louis H.
2012
BPS spectra and 3-manifold invariants. Zbl 1448.57020
Gukov, Sergei; Pei, Du; Putrov, Pavel; Vafa, Cumrun
2020
The Gordian complex of knots. Zbl 1004.57008
Hirasawa, Mikami; Uchida, Yoshiaki
2002
An invariant for singular knots. Zbl 1188.57010
Juyumaya, J.; Lambropoulou, S.
2009
Quandle colorings of knots and applications. Zbl 1302.57016
Clark, W. Edwin; Elhamdadi, Mohamed; Saito, Masahico; Yeatman, Timothy
2014
The planarity problem for signed Gauss words. Zbl 0821.57010
Cairns, Grant; Elton, Daniel M.
1993
Braids and the Nielsen-Thurston classification. Zbl 0874.57010
Bernardete, Diego; Nitecki, Zbigniew; Gutierrez, Mauricio
1995
The noncommutative A-ideal of a $$(2,2p+1)$$-torus knot determines its Jones polynomial. Zbl 1034.57005
Gelca, Răzvan; Sain, Jeremy
2003
Calculating Bar-Natan’s characteristic two Khovanov homology. Zbl 1114.57015
Turner, Paul R.
2006
Singular braids and Markov’s theorem. Zbl 0885.57005
Gemein, Bernd
1997
Vassiliev knot invariants coming from Lie algebras and 4-invariants. Zbl 0998.57034
Soboleva, E.
2001
Links with trivial Jones polynomial. Zbl 1001.57022
Thistlethwaite, Morwen
2001
Intrinsically $$n$$-linked graphs. Zbl 0998.57008
Flapan, Erica; Pommersheim, James; Foisy, Joel; Naimi, Ramin
2001
On random knots. Zbl 0846.57003
Diao, Yuanan; Pippenger, Nicholas; Sumners, De Witt
1994
Thistlethwaite’s theorem for virtual links. Zbl 1163.57001
Chmutov, Sergei; Voltz, Jeremy
2008
Boundedness and regularizing effects of O’Hara’s knot energies. Zbl 1238.57007
Blatt, Simon
2012
Topological quantum field theories associated to finite groups and crossed $$G$$-sets. Zbl 0770.57010
Yetter, David N.
1992
Geometric knot spaces and polygonal isotopy. Zbl 1001.57024
Calvo, Jorge Alberto
2001
Trace fields of twist knots. Zbl 1003.57014
Hoste, Jim; Shanahan, Patrick D.
2001
A construction of arbitrarily high degeneration of tunnel numbers of knots under connected sum. Zbl 0818.57006
Kobayashi, Tsuyoshi
1994
The knotting of equilateral polygons in $$\mathbb{R}^ 3$$. Zbl 0846.57004
Diao, Yuanan
1995
Topological properties of cyclically presented groups. Zbl 1031.57002
Cavicchioli, Alberto; Repovš, Dušan; Spaggiari, Fulvia
2003
On Habiro’s $$C_n$$-moves and Vassiliev invariants of order $$n$$. Zbl 0942.57011
Ohyama, Yoshiyuki; Tsukamoto, Tatsuya
1999
The simplest hyperbolic knots. Zbl 0933.57010
Callahan, Patrick J.; Dean, John C.; Weeks, Jeffrey R.
1999
Quantum groups at roots of unity and modularity. Zbl 1117.17006
Sawin, Stephen F.
2006
Markov trace on the Yokonuma-Hecke algebra. Zbl 1100.20008
Juyumaya, J.
2004
On the complex volume of hyperbolic knots. Zbl 1226.57025
Yokota, Yoshiyuki
2011
On the classification of quandles of low order. Zbl 1333.57026
Vendramin, L.
2012
The genus of closed 3-braids. Zbl 0773.57007
Xu, Peijun
1992
Braids, orderings and zero divisors. Zbl 0928.20031
Rolfsen, Dale; Zhu, Jun
1998
Studying surfaces via closed braids. Zbl 0907.57006
Birman, Joan S.; Finkelstein, Elizabeth
1998
A new point of view in the theory of knot and link invariants. Zbl 1002.57026
Labastida, José M. F.; Mariño, Marcos
2002
Colored ribbon Hopf algebras and universal invariants of framed links. Zbl 0798.57006
1993
Lissajous knots. Zbl 0834.57005
Bogle, M. G. V.; Hearst, J. E.; Jones, V. F. R.; Stoilov, L.
1994
Tangle decompositions of tunnel number one knots and links. Zbl 0841.57012
Gordon, C. McA.; Reid, A. W.
1995
On Khovanov’s cobordism theory for $$\mathfrak{su_3}$$ knot homology. Zbl 1300.57013
Morrison, Scott; Nieh, Ari
2008
Markov theorem for transversal links. Zbl 1046.57007
Orevkov, S. Yu.; Shevchishin, V. V.
2003
Geometric construction of modular functors from conformal field theory. Zbl 1123.81041
Andersen, Jørgen Ellegaard; Ueno, Kenji
2007
Hopfological algebra and categorification at a root of unity: the first steps. Zbl 1370.18017
Khovanov, Mikhail
2016
TQFT’s from homotopy 2-types. Zbl 0787.57002
Yetter, David N.
1993
Positive alternating links are positively alternating. Zbl 0999.57005
Nakamura, Takuji
2000
Virtual knot groups and their peripheral structure. Zbl 0997.57017
Kim, Se-Goo
2000
Long virtual knots and their invariants. Zbl 1064.57005
Manturov, Vassily O.
2004
Tied links in the solid torus. Zbl 1462.57004
Flores, Marcelo
2021
Group presentations for links in thickened surfaces. Zbl 07356494
Silver, Daniel S.; Williams, Susan G.
2021
The colored Jones polynomial and Kontsevich-Zagier series for double twist knots. Zbl 07373584
Lovejoy, Jeremy; Osburn, Robert
2021
BPS spectra and 3-manifold invariants. Zbl 1448.57020
Gukov, Sergei; Pei, Du; Putrov, Pavel; Vafa, Cumrun
2020
Large color $$R$$-matrix for knot complements and strange identities. Zbl 1460.57014
Park, Sunghyuk
2020
Planar pure braids on six strands. Zbl 07182541
Mostovoy, Jacob; Roque-Márquez, Christopher
2020
A lower bound of crosscap numbers of alternating knots. Zbl 1436.57006
Ito, Noboru; Takimura, Yusuke
2020
Multivariate Alexander quandles. I: The module sequence of a link. Zbl 1440.57011
Traldi, Lorenzo
2020
Refined Chern-Simons theory in genus two. Zbl 1450.57010
Arthamonov, S.; Shakirov, Sh.
2020
A note on coverings of virtual knots. Zbl 07243412
Nakamura, Takuji; Nakanishi, Yasutaka; Satoh, Shin
2020
Picture-valued parity-biquandle bracket. Zbl 1439.57028
Ilyutko, Denis P.; Manturov, Vassily O.
2020
Knot-theoretic flocks. Zbl 1448.57009
Niebrzydowski, Maciej; Pilitowska, Agata; Zamojska-Dzienio, Anna
2020
Raising crosscap number while lowering unknotting number. Zbl 1443.57003
Kerian, A.
2020
Mapping class group representations from Drinfeld doubles of finite groups. Zbl 1448.57018
2020
Erratum to: “Multivariate Alexander quandles. II. The involutory medial quandle of a link”. Zbl 1460.57007
Traldi, Lorenzo
2020
Cuspidal edges with the same first fundamental forms along a knot. Zbl 1455.57032
Honda, Atsufumi; Naokawa, Kosuke; Saji, Kentaro; Umehara, Masaaki; Yamada, Kotaro
2020
Crossing change on Khovanov homology and a categorified Vassiliev skein relation. Zbl 07243409
Ito, Noboru; Yoshida, Jun
2020
$$F$$-polynomials of tabulated virtual knots. Zbl 1447.57009
Ivanov, Maxim; Vesnin, Andrei
2020
On Bennequin-type inequalities for links in tight contact 3-manifolds. Zbl 1450.57005
Cavallo, Alberto
2020
Twisted torus knots $$T(p,q,p-kq,-1)$$ which are torus knots. Zbl 1452.57006
Lee, Sangyop
2020
3-manifolds with abelian embeddings in $$S^4$$. Zbl 1441.57022
Hillman, J. A.
2020
Some remarks on the chord index. Zbl 1464.57010
Cheng, Zhiyun; Gao, Hongzhu; Xu, Mengjian
2020
Some remarks on twin groups. Zbl 07291639
Naik, Tushar K.; Nanda, Neha; Singh, Mahender
2020
Triple-crossing projections, moves on knots and links and their minimal diagrams. Zbl 1444.57003
Jabłonowski, Michał; Trojanowski, Łukasz
2020
Variational formulae and estimates of O’Hara’s knot energies. Zbl 1441.53001
Kawakami, Shoya; Nagasawa, Takeyuki
2020
Functoriality of Khovanov homology. Zbl 07204975
Vogel, Pierre
2020
The knot Floer cube of resolutions and the composition product. Zbl 07205051
Dowlin, Nathan
2020
Knots with exactly 10 sticks. Zbl 1439.57005
Blair, Ryan; Eddy, Thomas D.; Morrison, Nathaniel; Shonkwiler, Clayton
2020
Biquandle coloring invariants of knotoids. Zbl 1428.57004
Gügümcü, Neslihan; Nelson, Sam
2019
Quandle coloring quivers. Zbl 1420.57032
Cho, Karina; Nelson, Sam
2019
Virtual tribrackets. Zbl 1426.57029
Nelson, Sam; Pico, Shane
2019
Finite-type invariants of order one of long and framed virtual knots. Zbl 1447.57010
Petit, Nicolas
2019
Transverse invariants from Khovanov-type homologies. Zbl 1409.57004
Collari, Carlo
2019
Multivariate Alexander quandles. III. Sublinks. Zbl 1436.57011
Traldi, Lorenzo
2019
Artin’s braids, braids for three space, and groups $${\Gamma}_n^4$$ and $$G_n^k$$. Zbl 1431.57005
Kim, Seongjeong; Manturov, V. O.
2019
Triple-crossing number and moves on triple-crossing link diagrams. Zbl 1431.57001
Adams, Colin; Hoste, Jim; Palmer, Martin
2019
Biquandle virtual brackets. Zbl 1436.57014
Nelson, Sam; Oshiro, Kanako; Shimizu, Ayaka; Yaguchi, Yoshiro
2019
An important step for the computation of the HOMFLYPT skein module of the Lens spaces $$L(p, 1)$$ via braids. Zbl 1452.57005
Diamantis, Ioannis; Lambropoulou, Sofia
2019
An explicit symmetric DGLA model of a bi-gon. Zbl 07139445
Gadish, Nir; Griniasty, Itay; Lawrence, Ruth
2019
Tg-hyperbolicity of virtual links. Zbl 07167000
Adams, Colin; Eisenberg, Or; Greenberg, Jonah; Kapoor, Kabir; Liang, Zhen; O&rsquo;Connor, Kate; Pacheco-Tallaj, Natalia; Wang, Yi
2019
Universal knot diagrams. Zbl 1440.57002
Even-Zohar, Chaim; Hass, Joel; Linial, Nati; Nowik, Tahl
2019
Constructing a polynomial whose nodal set is any prescribed knot or link. Zbl 1411.57010
Bode, Benjamin; Dennis, Mark R.
2019
Constructing links of isolated singularities of polynomials $$\mathbb{R}^4 \rightarrow \mathbb{R}^2$$. Zbl 1411.57009
Bode, Benjamin
2019
Triple crossing number and double crossing braid index. Zbl 1410.57008
Nishida, Daishiro
2019
Graph polynomials and link invariants as positive type functions on Thompson’s group $$F$$. Zbl 1412.43007
Aiello, Valeriano; Conti, Roberto
2019
$$L$$-spaces, left-orderability and two-bridge knots. Zbl 1422.57009
Ba, Idrissa
2019
Positively twisted torus knots which are torus knots. Zbl 1426.57014
Lee, Sangyop
2019
Rail knotoids. Zbl 1436.57008
Kodokostas, Dimitrios; Lambropoulou, Sofia
2019
Rectangle condition for bridge decompositions of links. Zbl 1435.57004
Kwon, Bo-Hyun
2019
A bridge between Conway-Coxeter friezes and rational tangles through the Kauffman bracket polynomials. Zbl 1436.57009
Kogiso, Takeyoshi; Wakui, Michihisa
2019
The ropelengths of knots are almost linear in terms of their crossing numbers. Zbl 1441.57006
Diao, Yuanan; Ernst, Claus; Por, Attila; Ziegler, Uta
2019
Cable knots do not admit cosmetic surgeries. Zbl 1429.57007
Tao, Ran
2019
Classification of ribbon 2-knots presented by virtual arcs with up to four crossings. Zbl 1429.57017
Kanenobu, Taizo; Sumi, Toshio
2019
Jabłonowski, Michał
2019
A new two-variable generalization of the Jones polynomial. Zbl 1432.57024
Goundaroulis, Dimos; Lambropoulou, Sofia
2019
Infinitesimal bending of knots and energy change. Zbl 1429.53004
Kauffman, Louis H.; Velimirović, Ljubica S.; Najdanović, Marija S.; Rančić, Svetozar R.
2019
Virtualization and $$n$$-writhes for virtual knots. Zbl 1444.57010
Ohyama, Yoshiyuki; Sakurai, Migiwa
2019
Continuous cohomology of topological quandles. Zbl 1432.57011
Elhamdadi, Mohamed; Saito, Masahico; Zappala, Emanuele
2019
Virtual Seifert surfaces. Zbl 1422.57017
Chrisman, Micah
2019
An ergodic algorithm for generating knots with a prescribed injectivity radius. Zbl 1429.57004
Chapman, Kyle Leland
2019
Virtual tangles and fiber functors. Zbl 1460.57012
2019
A simple proof of the strong integrality for full colored HOMFLYPT invariants. Zbl 1426.57033
Zhu, Shengmao
2019
Minimal coloring number for $$\mathbb{Z}$$-colorable links. II. Zbl 1419.57018
Matsudo, Eri
2019
The Alexander polynomial of links in Lens spaces. Zbl 1422.57022
Horvat, E.; Gabrovšek, Boštjan
2019
Stability properties of the colored Jones polynomial. Zbl 1444.57005
Lee, Christine Ruey Shan
2019
Ascending number and Conway polynomial. Zbl 1426.57009
Higa, Ryuji
2019
Knot invariants from Laplacian matrices. Zbl 1423.57020
Silver, Daniel S.; Williams, Susan G.
2019
Alexander- and Markov-type theorems for virtual trivalent braids. Zbl 1418.57003
Caprau, Carmen; Dirdak, Abigayle; Post, Rita; Sawyer, Erica
2019
The total curvature of knots under second-order infinitesimal bending. Zbl 1410.53005
Najdanović, Marija S.; Rančić, Svetozar R.; Kauffman, Louis H.; Velimirović, Ljubica S.
2019
Cubulated moves for 2-knots. Zbl 1409.57026
Díaz, Juan Pablo; Hinojosa, Gabriela; Verjosvky, Alberto
2019
Infinite families of prime knots with $$\mathrm{alt}(K) = 1$$ and their Alexander polynomials. Zbl 1412.57004
de los Angeles Guevara Hernández, María; Cabrera Ibarra, Hugo
2019
Families of not perfectly straight knots. Zbl 1422.57027
2019
Finite $$n$$-quandles of torus and two-bridge links. Zbl 1418.57005
Crans, Alissa S.; Mellor, Blake; Shanahan, Patrick D.; Hoste, Jim
2019
Quasirationality and prounipotent crossed modules. Zbl 07177775
Mikhovich, A. M.
2019
The Kauffman bracket skein module of the handlebody of genus 2 via braids. Zbl 07177783
Diamantis, Ioannis
2019
Properties of minimal charts and their applications. V. Charts of type $$(3,2,2)$$. Zbl 1434.57016
Nagase, Teruo; Shima, Akiko
2019
Oriented local moves and divisibility of the Jones-Kauffman polynomial. Zbl 1436.57002
Drube, Paul; Pongtanapaisan, Puttipong
2019
Classification of Legendrian knots of topological type $$7_6$$ with maximal Thurston-Bennequin number. Zbl 1436.57003
Dynnikov, Ivan; Prasolov, Maxim
2019
Solutions of the Yang-Baxter equation associated to skew left braces, with applications to racks. Zbl 1443.16040
Bachiller, David
2018
Generating sets of Reidemeister moves of oriented singular links and quandles. Zbl 1414.57004
Bataineh, Khaled; Elhamdadi, Mohamed; Hajij, Mustafa; Youmans, William
2018
Two-variable polynomial invariants of virtual knots arising from flat virtual knot invariants. Zbl 1428.57005
Kaur, Kirandeep; Prabhakar, Madeti; Vesnin, Andrei
2018
Doodles on surfaces. Zbl 1403.57003
2018
Boltzmann enhancements of biquasile counting invariants. Zbl 1411.57023
Choi, Wonhyuk; Needell, Deanna; Nelson, Sam
2018
Virtual knot cobordism and the affine index polynomial. Zbl 1436.57007
Kauffman, Louis H.
2018
The Legendrian knot complement problem. Zbl 1467.53088
Kegel, Marc
2018
The structure of a minimal $$n$$-chart with two crossings. I: Complementary domains of $${\Gamma}_1 \cup {\Gamma}_{n - 1}$$. Zbl 1408.57025
Nagase, Teruo; Shima, Akiko
2018
Twisted Alexander polynomials of 2-bridge knots associated to dihedral representations. Zbl 1385.57009
Hirasawa, Mikami; Murasugi, Kunio
2018
An invariant of virtual knots using flat virtual knot diagrams. Zbl 1387.57012
Kim, Joonoh; Shin, Mihaw
2018
Quasi-trivial quandles and biquandles, cocycle enhancements and link-homotopy of pretzel links. Zbl 06966581
Elhamdadi, Mohamed; Liu, Minghui; Nelson, Sam
2018
On independence of iterated Whitehead doubles in the knot concordance group. Zbl 1395.53093
Park, Kyungbae
2018
Presentation of immersed surface-links by marked graph diagrams. Zbl 1401.57035
Kamada, Seiichi; Kawauchi, Akio; Kim, Jieon; Lee, Sang Youl
2018
On unrolled Hopf algebras. Zbl 1434.16016
Andruskiewitsch, Nicolás; Schweigert, Christoph
2018
Multivariate Alexander colorings. Zbl 1405.57018
Traldi, Lorenzo
2018
Bridge spectra of cables of 2-bridge knots. Zbl 1386.57012
2018
On the generalization of Conway algebra. Zbl 1385.57016
Kim, Seongjeong
2018
Verification of the Jones unknot conjecture up to 22 crossings. Zbl 1386.57016
Tuzun, Robert E.; Sikora, Adam S.
2018
Simplifying branched covering surface-knots by an addition of 1-handles with chart loops. Zbl 1394.57021
Nakamura, Inasa
2018
Fox formulas for twisted Alexander invariants associated to representations of knot groups over rings of $$S$$-integers. Zbl 1392.57008
Tange, Ryoto
2018
Equivalence of two definitions of set-theoretic Yang-Baxter homology and general Yang-Baxter homology. Zbl 1398.57019
Przytycki, Józef H.; Wang, Xiao
2018
A note on the Gordian complexes of some local moves on knots. Zbl 1400.57013
Zhang, Kai; Yang, Zhiqing
2018
...and 1234 more Documents
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#### Cited by 3,336 Authors

 81 Kauffman, Louis Hirsch 56 Nelson, Sam 52 Manturov, Vassiliĭ Olegovich 44 Kamada, Seiichi 39 Stoimenow, Alexander 37 Saito, Masahico 31 Garoufalidis, Stavros 31 Przytycki, Józef H. 30 Elhamdadi, Mohamed 29 Diao, Yuanan 29 Morozov, Alexei Yurievich 28 Carter, J. Scott 28 Kawauchi, Akio 28 Lee, Sang Youl 28 Satoh, Shin 26 Kanenobu, Taizo 26 Lambropoulou, Sofia S. F. 26 Oh, Seungsang 26 Silver, Daniel S. 25 Adams, Colin C. 25 Bardakov, Valeriĭ Georgievich 25 Jin, Xian’an 24 Williams, Susan G. 23 Ito, Tetsuya 23 Mironov, Andrei D. 22 Ito, Noboru 22 Kamada, Naoko 22 Ozawa, Makoto 22 Yasuhara, Akira 21 Im, Young Ho 21 Le, Thang Tu Quoc 21 Nakanishi, Yasutaka 21 Patureau-Mirand, Bertrand 21 Tran, Anh Tuan 20 East, James 20 Ernst, Claus 20 Geer, Nathan 20 Ishii, Atsushi 20 Mellor, Blake 19 Ichihara, Kazuhiro 19 Orevkov, Stepan Yur’evich 19 Spaggiari, Fulvia 18 Cavicchioli, Alberto 18 Jablan, Slavik Vlado 18 Oshiro, Kanako 18 Traldi, Lorenzo 17 Andersen, Jørgen Ellegaard 17 Bae, Yongju 17 Nikkuni, Ryo 17 Ohyama, Yoshiyuki 17 Shimizu, Ayaka 17 Xue, Kang 16 Bellingeri, Paolo 16 Chbili, Nafaa 16 Dehornoy, Patrick 16 Frohman, Charles D. 16 Guaschi, John 16 Lei, Fengchun 16 Mattman, Thomas W. 16 Meilhan, Jean-Baptiste 15 Cheng, Zhiyun 15 Jeong, Myeong-Ju 15 Lopes, Pedro 15 Nakamura, Takuji 14 Dye, Heather Ann 14 Eudave-Muñoz, Mario 14 Fleming, Thomas R. 14 Gonçalves, Daciberg Lima 14 Hoste, Jim 14 Jin, Gyo Taek 14 Martin, Paul Purdon 14 Motegi, Kimihiko 14 Ramadevi, Pichai 14 Rowell, Eric C. 14 Vesnin, Andrei Yu. 14 Wang, Zhenghan 13 Baker, Kenneth L. 13 Boden, Hans U. 13 Chrisman, Micah Whitney 13 Hedden, Matthew 13 Kadokami, Teruhisa 13 Kalfagianni, Efstratia 13 Khovanov, Mikhail G. 13 Kofman, Ilya 13 Lauda, Aaron D. 13 Lebed, Victoria 13 Lee, Hwa Jeong 13 Moffatt, Iain 13 Murakami, Jun 13 Sazdanović, Radmila 13 Shima, Akiko 13 Taniyama, Kouki 12 Champanerkar, Abhijit 12 Chmutov, Sergei V. 12 Cristofori, Paola 12 Gilmer, Patrick M. 12 González-Meneses, Juan 12 Gukov, Sergei 12 Hayashi, Chuichiro 12 Hikami, Kazuhiro ...and 3,236 more Authors
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#### Cited in 356 Journals

 1,346 Journal of Knot Theory and its Ramifications 377 Topology and its Applications 280 Algebraic & Geometric Topology 109 Proceedings of the American Mathematical Society 109 Transactions of the American Mathematical Society 106 Journal of Algebra 101 Advances in Mathematics 83 Communications in Mathematical Physics 72 Journal of Pure and Applied Algebra 71 Geometry & Topology 61 Journal of High Energy Physics 59 Osaka Journal of Mathematics 53 Quantum Topology 52 International Journal of Mathematics 48 Journal of Mathematical Physics 48 Mathematical Proceedings of the Cambridge Philosophical Society 47 Geometriae Dedicata 43 Communications in Algebra 33 Mathematische Zeitschrift 33 European Journal of Combinatorics 32 Journal of Mathematical Sciences (New York) 30 Letters in Mathematical Physics 30 Journal of Geometry and Physics 29 Journal of the Mathematical Society of Japan 29 Mathematische Annalen 29 Tokyo Journal of Mathematics 26 Experimental Mathematics 25 Nuclear Physics. B 25 Journal of Algebraic Combinatorics 23 Discrete Mathematics 22 Journal of Combinatorial Theory. Series A 22 International Journal of Algebra and Computation 21 Quantum Information Processing 20 Inventiones Mathematicae 18 Duke Mathematical Journal 18 Advances in Applied Mathematics 17 Chaos, Solitons and Fractals 16 Selecta Mathematica. New Series 15 Acta Mathematica Vietnamica 15 Annales de l’Institut Fourier 15 Journal of Algebra and its Applications 14 International Journal of Modern Physics A 14 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 14 Proceedings of the Steklov Institute of Mathematics 14 Journal of Topology 13 Bulletin of the Australian Mathematical Society 13 Israel Journal of Mathematics 13 Boletín de la Sociedad Matemática Mexicana. Third Series 13 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 12 Michigan Mathematical Journal 12 Siberian Mathematical Journal 12 Discrete & Computational Geometry 12 Forum Mathematicum 12 Bulletin of the American Mathematical Society. New Series 12 Algebras and Representation Theory 12 Communications in Contemporary Mathematics 12 Journal of the Australian Mathematical Society 12 Comptes Rendus. Mathématique. Académie des Sciences, Paris 12 Mediterranean Journal of Mathematics 11 Compositio Mathematica 11 Fundamenta Mathematicae 11 Manuscripta Mathematica 11 Pacific Journal of Mathematics 11 Annales Henri Poincaré 11 Journal of Physics A: Mathematical and Theoretical 10 Theoretical and Mathematical Physics 10 Acta Mathematica Sinica. English Series 9 Discrete Applied Mathematics 9 Glasgow Mathematical Journal 9 Journal of Symbolic Computation 9 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 9 Journal of Topology and Analysis 9 Winter Braids Lecture Notes 8 Journal of Statistical Physics 8 Mathematical Notes 8 Journal of Combinatorial Theory. Series B 8 Semigroup Forum 8 The New York Journal of Mathematics 8 Journal of Mathematical Chemistry 8 Doklady Mathematics 8 Groups, Geometry, and Dynamics 7 Reviews in Mathematical Physics 7 Journal of Graph Theory 7 Journal of the London Mathematical Society. Second Series 7 Proceedings of the Edinburgh Mathematical Society. Series II 7 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 7 Journal of the European Mathematical Society (JEMS) 7 Journal of Homotopy and Related Structures 7 Arnold Mathematical Journal 6 International Journal of Theoretical Physics 6 Journal of Mathematical Biology 6 Applied Mathematics and Computation 6 Functional Analysis and its Applications 6 Indiana University Mathematics Journal 6 International Journal of Mathematics and Mathematical Sciences 6 Journal für die Reine und Angewandte Mathematik 6 Kyungpook Mathematical Journal 6 Proceedings of the Japan Academy. Series A 6 Chinese Annals of Mathematics. Series B 6 Graphs and Combinatorics ...and 256 more Journals
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#### Cited in 58 Fields

 3,746 Manifolds and cell complexes (57-XX) 802 Group theory and generalizations (20-XX) 465 Quantum theory (81-XX) 448 Combinatorics (05-XX) 299 Associative rings and algebras (16-XX) 256 Nonassociative rings and algebras (17-XX) 224 Category theory; homological algebra (18-XX) 201 Differential geometry (53-XX) 180 Algebraic geometry (14-XX) 174 Algebraic topology (55-XX) 140 Global analysis, analysis on manifolds (58-XX) 101 Dynamical systems and ergodic theory (37-XX) 82 Number theory (11-XX) 82 Computer science (68-XX) 69 Functional analysis (46-XX) 67 Several complex variables and analytic spaces (32-XX) 67 Relativity and gravitational theory (83-XX) 66 Biology and other natural sciences (92-XX) 64 Statistical mechanics, structure of matter (82-XX) 50 Order, lattices, ordered algebraic structures (06-XX) 42 Probability theory and stochastic processes (60-XX) 34 Topological groups, Lie groups (22-XX) 33 Functions of a complex variable (30-XX) 32 Geometry (51-XX) 31 Convex and discrete geometry (52-XX) 30 Commutative algebra (13-XX) 28 Special functions (33-XX) 28 Calculus of variations and optimal control; optimization (49-XX) 27 General algebraic systems (08-XX) 27 Linear and multilinear algebra; matrix theory (15-XX) 21 Numerical analysis (65-XX) 19 Mathematical logic and foundations (03-XX) 19 General topology (54-XX) 18 Partial differential equations (35-XX) 13 $$K$$-theory (19-XX) 13 Fluid mechanics (76-XX) 12 Field theory and polynomials (12-XX) 12 Information and communication theory, circuits (94-XX) 11 Mechanics of deformable solids (74-XX) 10 History and biography (01-XX) 10 Measure and integration (28-XX) 10 Statistics (62-XX) 9 General and overarching topics; collections (00-XX) 9 Real functions (26-XX) 8 Optics, electromagnetic theory (78-XX) 7 Ordinary differential equations (34-XX) 7 Approximations and expansions (41-XX) 7 Mechanics of particles and systems (70-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Systems theory; control (93-XX) 5 Difference and functional equations (39-XX) 3 Abstract harmonic analysis (43-XX) 2 Operator theory (47-XX) 2 Operations research, mathematical programming (90-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Potential theory (31-XX) 1 Integral equations (45-XX) 1 Mathematics education (97-XX)