# zbMATH — the first resource for mathematics

## Fenn, Roger A.

Compute Distance To:
 Author ID: fenn.roger-a Published as: Fenn, R.; Fenn, R. A.; Fenn, Roger; Fenn, Roger A.
 Documents Indexed: 60 Publications since 1970, including 4 Books Reviewing Activity: 10 Reviews
all top 5

#### Co-Authors

 14 single-authored 13 Rourke, Colin P. 4 Sanderson, Brian J. 4 Sjerve, Denis K. 3 Bartholomew, Andrew 3 Kauffman, Louis Hirsch 3 Rimányi, Richárd 3 Rolfsen, Dale 2 Budden, Stephen 2 Keyman, Ebru 2 Manturov, Vassiliĭ Olegovich 1 Azcan, Hüseyin 1 Cervantes, Leticia 1 Dunwoody, Martin John 1 Greene, Michael T. 1 Hilton, Peter John 1 Ibáñez-Varela, Raúl 1 Il’yutko, Denis Petrovich 1 Jin, Gyo Taek 1 Jordan-Santana, Mercedes 1 Kamada, Naoko 1 Kamada, Seiichi 1 Taylor, Paul H. 1 Turaev, Vladimir G. 1 Wiest, Bertold 1 Zhu, Jun
all top 5

#### Serials

 9 Journal of Knot Theory and its Ramifications 3 Topology 2 Bulletin of the London Mathematical Society 2 Canadian Journal of Mathematics 2 Fundamenta Mathematicae 2 Pacific Journal of Mathematics 2 L’Enseignement Mathématique. 2e Série 2 Turkish Journal of Mathematics 2 London Mathematical Society Lecture Note Series 1 Journal of Geometry and Physics 1 Journal of the London Mathematical Society. Second Series 1 Osaka Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 The Quarterly Journal of Mathematics. Oxford Second Series 1 Transactions of the American Mathematical Society 1 Topology and its Applications 1 Kobe Journal of Mathematics 1 Publicacions Matemàtiques 1 Forum Mathematicum 1 Applied Categorical Structures 1 Lecture Notes in Mathematics
all top 5

#### Fields

 47 Manifolds and cell complexes (57-XX) 15 Group theory and generalizations (20-XX) 8 Algebraic topology (55-XX) 2 General and overarching topics; collections (00-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Geometry (51-XX)

#### Citations contained in zbMATH

47 Publications have been cited 828 times in 566 Documents Cited by Year
Racks and links in codimension two. Zbl 0787.57003
Fenn, Roger; Rourke, Colin
1992
Trunks and classifying spaces. Zbl 0853.55021
Fenn, Roger; Rourke, Colin; Sanderson, Brian
1995
The braid-permutation group. Zbl 0861.57010
Fenn, Roger; Rimányi, Richárd; Rourke, Colin
1997
Biquandles and virtual links. Zbl 1063.57006
Fenn, Roger; Jordan-Santana, Mercedes; Kauffman, Louis
2004
James bundles. Zbl 1055.55005
Fenn, Roger; Rourke, Colin; Sanderson, Brian
2004
On Kirby’s calculus of links. Zbl 0413.57006
Fenn, Roger; Rourke, Colin
1979
Techniques of geometric topology. Zbl 0517.57001
Fenn, Roger A.
1983
The rack space. Zbl 1123.55006
Fenn, Roger; Rourke, Colin; Sanderson, Brian
2007
Virtual knot theory – unsolved problems. Zbl 1084.57005
Fenn, Roger; Kauffman, Louis H.; Manturov, Vassily O.
2005
Ordering the braid groups. Zbl 1009.20042
Fenn, R.; Greene, M. T.; Rolfsen, D.; Rourke, C.; Wiest, B.
1999
Quaternionic invariants of virtual knots and links. Zbl 1149.57301
Bartholomew, Andrew; Fenn, Roger
2008
An introduction to species and the rack space. Zbl 0828.57005
Fenn, Roger; Rourke, Colin; Sanderson, Brian
1993
Centralisers in the braid group and singular braid monoid. Zbl 0869.20024
Fenn, Roger; Rolfsen, Dale; Zhu, Jun
1996
The singular baid monoid embeds in a group. Zbl 0971.57011
Fenn, Roger; Keyman, Ebru; Rourke, Colin
1998
Weyl algebras and knots. Zbl 1123.57006
2007
The equation $$[B,(A-1)(A,B)]=0$$ and virtual knots and links. Zbl 1070.57003
Budden, Stephen; Fenn, Roger
2004
Spheres may link homotopically in 4-space. Zbl 0603.57011
Fenn, Roger; Rolfsen, Dale
1986
Klyachko’s methods and the solution of equations over torsion-free groups. Zbl 0861.20029
Fenn, Roger; Rourke, Colin
1996
Doodles on surfaces. Zbl 1403.57003
2018
Introducing doodles. Zbl 0409.57003
Fenn, Roger; Taylor, Paul
1979
Biquandles of small size and some invariants of virtual and welded knots. Zbl 1226.57006
Bartholomew, Andrew; Fenn, Roger
2011
Massey products and lower central series of free groups. Zbl 0643.57002
Fenn, Roger; Sjerve, Denis
1987
Unsolved problems in virtual knot theory and combinatorial knot theory. Zbl 1310.57010
Fenn, Roger; Ilyutko, Denis P.; Kauffman, Louis H.; Manturov, Vassily O.
2014
Tackling the trefoils. Zbl 1275.57008
Fenn, Roger
2012
Some remarks on the braid-permutation group. Zbl 0830.57005
Fenn, Roger; Rimányi, Richárd; Rourke, Colin
1993
The table theorem. Zbl 0194.53901
Fenn, Roger
1970
Quaternion algebras and invariants of virtual knots and links I: the elliptic case. Zbl 1158.57008
Fenn, Roger
2008
Characterisation of a class of equations with solutions over torsion-free groups. Zbl 0913.20018
Fenn, Roger; Rourke, Colin
1998
Boundary links are homotopy trivial. Zbl 0655.57003
Cervantes, L.; Fenn, R. A.
1988
On the finiteness of higher knot sums. Zbl 0623.57013
Dunwoody, M. J.; Fenn, R. A.
1987
Basic commutators and minimal Massey products. Zbl 0561.55015
Fenn, Roger; Sjerve, Denis
1984
Colorings and doubled colorings of virtual doodles. Zbl 1419.57022
2019
Generalised biquandles for generalised knot theories. Zbl 1409.57006
Fenn, Roger
2015
Some generalizations of the Borsuk-Ulam theorem and applications to realizing homotopy classes by embedded spheres. Zbl 0268.55008
Fenn, Roger
1973
On Gauss codes of virtual doodles. Zbl 1411.57007
2018
Biquandles and their application to virtual knots and links. Zbl 1180.57021
Fenn, Roger
2009
Quaternion algebras and invariants of virtual knots and links II: the hyperbolic case. Zbl 1159.57002
Budden, Stephen; Fenn, Roger
2008
Nice spines of 3-manifolds. Zbl 0406.57002
Fenn, Roger; Rourke, Colin
1979
On Dehn’s lemma in 4 dimensions. Zbl 0215.52003
Fenn, R.
1971
Embedding polyhedra. Zbl 0207.53105
Fenn, R.
1970
New invariants of long virtual knots. Zbl 1260.57004
2010
Geometry. Zbl 0959.51001
Fenn, Roger
2001
Vassiliev theory for knots. Zbl 0865.57006
Fenn, Roger
1994
What is the geometry of a surface? Zbl 0528.57006
Fenn, Roger
1983
Geometric cohomology theory. Zbl 0522.55008
Fenn, Roger; Sjerve, Denis
1983
Duality and cohomology for one relator groups. Zbl 0518.20041
Fenn, Roger; Sjerve, Denis
1982
Some applications of the width and breadth of a closed curve to the two- dimensional sphere. Zbl 0301.50005
Fenn, Roger
1975
Colorings and doubled colorings of virtual doodles. Zbl 1419.57022
2019
Doodles on surfaces. Zbl 1403.57003
2018
On Gauss codes of virtual doodles. Zbl 1411.57007
2018
Generalised biquandles for generalised knot theories. Zbl 1409.57006
Fenn, Roger
2015
Unsolved problems in virtual knot theory and combinatorial knot theory. Zbl 1310.57010
Fenn, Roger; Ilyutko, Denis P.; Kauffman, Louis H.; Manturov, Vassily O.
2014
Tackling the trefoils. Zbl 1275.57008
Fenn, Roger
2012
Biquandles of small size and some invariants of virtual and welded knots. Zbl 1226.57006
Bartholomew, Andrew; Fenn, Roger
2011
New invariants of long virtual knots. Zbl 1260.57004
2010
Biquandles and their application to virtual knots and links. Zbl 1180.57021
Fenn, Roger
2009
Quaternionic invariants of virtual knots and links. Zbl 1149.57301
Bartholomew, Andrew; Fenn, Roger
2008
Quaternion algebras and invariants of virtual knots and links I: the elliptic case. Zbl 1158.57008
Fenn, Roger
2008
Quaternion algebras and invariants of virtual knots and links II: the hyperbolic case. Zbl 1159.57002
Budden, Stephen; Fenn, Roger
2008
The rack space. Zbl 1123.55006
Fenn, Roger; Rourke, Colin; Sanderson, Brian
2007
Weyl algebras and knots. Zbl 1123.57006
2007
Virtual knot theory – unsolved problems. Zbl 1084.57005
Fenn, Roger; Kauffman, Louis H.; Manturov, Vassily O.
2005
Biquandles and virtual links. Zbl 1063.57006
Fenn, Roger; Jordan-Santana, Mercedes; Kauffman, Louis
2004
James bundles. Zbl 1055.55005
Fenn, Roger; Rourke, Colin; Sanderson, Brian
2004
The equation $$[B,(A-1)(A,B)]=0$$ and virtual knots and links. Zbl 1070.57003
Budden, Stephen; Fenn, Roger
2004
Geometry. Zbl 0959.51001
Fenn, Roger
2001
Ordering the braid groups. Zbl 1009.20042
Fenn, R.; Greene, M. T.; Rolfsen, D.; Rourke, C.; Wiest, B.
1999
The singular baid monoid embeds in a group. Zbl 0971.57011
Fenn, Roger; Keyman, Ebru; Rourke, Colin
1998
Characterisation of a class of equations with solutions over torsion-free groups. Zbl 0913.20018
Fenn, Roger; Rourke, Colin
1998
The braid-permutation group. Zbl 0861.57010
Fenn, Roger; Rimányi, Richárd; Rourke, Colin
1997
Centralisers in the braid group and singular braid monoid. Zbl 0869.20024
Fenn, Roger; Rolfsen, Dale; Zhu, Jun
1996
Klyachko’s methods and the solution of equations over torsion-free groups. Zbl 0861.20029
Fenn, Roger; Rourke, Colin
1996
Trunks and classifying spaces. Zbl 0853.55021
Fenn, Roger; Rourke, Colin; Sanderson, Brian
1995
Vassiliev theory for knots. Zbl 0865.57006
Fenn, Roger
1994
An introduction to species and the rack space. Zbl 0828.57005
Fenn, Roger; Rourke, Colin; Sanderson, Brian
1993
Some remarks on the braid-permutation group. Zbl 0830.57005
Fenn, Roger; Rimányi, Richárd; Rourke, Colin
1993
Racks and links in codimension two. Zbl 0787.57003
Fenn, Roger; Rourke, Colin
1992
Boundary links are homotopy trivial. Zbl 0655.57003
Cervantes, L.; Fenn, R. A.
1988
Massey products and lower central series of free groups. Zbl 0643.57002
Fenn, Roger; Sjerve, Denis
1987
On the finiteness of higher knot sums. Zbl 0623.57013
Dunwoody, M. J.; Fenn, R. A.
1987
Spheres may link homotopically in 4-space. Zbl 0603.57011
Fenn, Roger; Rolfsen, Dale
1986
Basic commutators and minimal Massey products. Zbl 0561.55015
Fenn, Roger; Sjerve, Denis
1984
Techniques of geometric topology. Zbl 0517.57001
Fenn, Roger A.
1983
What is the geometry of a surface? Zbl 0528.57006
Fenn, Roger
1983
Geometric cohomology theory. Zbl 0522.55008
Fenn, Roger; Sjerve, Denis
1983
Duality and cohomology for one relator groups. Zbl 0518.20041
Fenn, Roger; Sjerve, Denis
1982
On Kirby’s calculus of links. Zbl 0413.57006
Fenn, Roger; Rourke, Colin
1979
Introducing doodles. Zbl 0409.57003
Fenn, Roger; Taylor, Paul
1979
Nice spines of 3-manifolds. Zbl 0406.57002
Fenn, Roger; Rourke, Colin
1979
Some applications of the width and breadth of a closed curve to the two- dimensional sphere. Zbl 0301.50005
Fenn, Roger
1975
Some generalizations of the Borsuk-Ulam theorem and applications to realizing homotopy classes by embedded spheres. Zbl 0268.55008
Fenn, Roger
1973
On Dehn’s lemma in 4 dimensions. Zbl 0215.52003
Fenn, R.
1971
The table theorem. Zbl 0194.53901
Fenn, Roger
1970
Embedding polyhedra. Zbl 0207.53105
Fenn, R.
1970
all top 5

#### Cited by 511 Authors

 40 Nelson, Sam 21 Kamada, Seiichi 20 Kauffman, Louis Hirsch 20 Saito, Masahico 19 Przytycki, Józef H. 17 Carter, J. Scott 15 Manturov, Vassiliĭ Olegovich 14 Bardakov, Valeriĭ Georgievich 12 Lebed, Victoria 12 Oshiro, Kanako 11 Elhamdadi, Mohamed 11 Fenn, Roger A. 11 Nosaka, Takefumi 10 Dehornoy, Patrick 10 Satoh, Shin 9 Bellingeri, Paolo 8 Niebrzydowski, Maciej 7 Ito, Tetsuya 6 Bartholomew, Andrew 6 Crans, Alissa S. 6 Kamada, Naoko 6 Lambropoulou, Sofia S. F. 6 Lee, Sang Youl 6 Vendramin, Leandro 6 Vershinin, Vladimir V. 6 Wiest, Bertold 5 Clark, W. Edwin 5 Dye, Heather Ann 5 Horvat, Eva 5 Ishii, Atsushi 5 Iwakiri, Masahide 5 Jelsovsky, Daniel 5 Nasybullov, Timur Rinatovich 5 Paris, Luis 5 Rourke, Colin P. 5 Singh, Mahender 5 Turaev, Vladimir G. 5 Yang, Seung Yeop 5 Yasuhara, Akira 4 Bae, Yongju 4 Cheng, Zhiyun 4 Chrisman, Micah Whitney 4 Dabkowski, Mieczysław K. 4 Efrat, Ido 4 Hoste, Jim 4 Il’yutko, Denis Petrovich 4 Kim, Jieon 4 Lopes, Pedro 4 Mináč, Ján 4 Mukherjee, Sujoy 4 Nakanishi, Yasutaka 4 Nguyêñ Duy Tân 4 Rolfsen, Dale 4 Rump, Wolfgang 4 Sanderson, Brian J. 4 Shanahan, Patrick D. 4 Tanaka, Kokoro 4 Wagemann, Friedrich 3 Damiani, Celeste 3 Eisermann, Michael 3 Farinati, Marco Andrés 3 Gao, Hongzhu 3 Garoufalidis, Stavros 3 Godelle, Eddy 3 Gongopadhyay, Krishnendu 3 González-Meneses, Juan 3 Habiro, Kazuo 3 Inoue, Ayumu 3 Jedlička, Přemysl 3 Kaestner, Aaron M. 3 Kim, Byeorhi 3 Kim, Joonoh 3 Klyachko, Anton Aleksandrovich 3 Koschorke, Ulrich 3 Melikhov, Sergey Aleksandrovich 3 Melvin, Paul M. 3 Nanda, Neha 3 Neshchadim, Mikhail Vladimirovich 3 Ohtsuki, Tomotada 3 Oyamaguchi, Natsumi 3 Pilitowska, Agata 3 Rosebrock, Stephan 3 Stanovský, David 3 Suciu, Alexander I. 3 Wada, Kodai 3 Winter, Blake Karl 3 Zamojska-Dzienio, Anna 2 Afanasiev, Denis Mikhailovich 2 Altschuler, Daniel 2 Antony, Noelle 2 Ashihara, Sosuke 2 Audoux, Benjamin 2 Benedetti, Riccardo 2 Bonatto, Marco 2 Calvez, Matthieu 2 Cattabriga, Alessia 2 Ceniceros, Jose 2 Churchill, Indu R. U. 2 Corran, Ruth 2 Coste, Antoine D. ...and 411 more Authors
all top 5

#### Cited in 112 Serials

 172 Journal of Knot Theory and its Ramifications 43 Topology and its Applications 24 Algebraic & Geometric Topology 20 Journal of Pure and Applied Algebra 19 Journal of Algebra 19 Transactions of the American Mathematical Society 15 Communications in Algebra 12 Advances in Mathematics 10 Geometry & Topology 9 International Journal of Mathematics 8 Inventiones Mathematicae 8 Proceedings of the American Mathematical Society 8 International Journal of Algebra and Computation 8 Journal of Algebra and its Applications 6 Communications in Mathematical Physics 6 Mathematische Zeitschrift 6 Osaka Journal of Mathematics 5 Geometriae Dedicata 5 Mathematische Annalen 5 Proceedings of the Steklov Institute of Mathematics 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Journal of Geometry and Physics 4 Journal of Mathematical Sciences (New York) 4 Annales Mathématiques Blaise Pascal 4 Journal of Group Theory 3 Journal of Mathematical Physics 3 Annales de l’Institut Fourier 3 Journal of Combinatorial Theory. Series B 3 Journal of the Mathematical Society of Japan 3 Manuscripta Mathematica 3 Siberian Mathematical Journal 3 European Journal of Combinatorics 3 Forum Mathematicum 2 Mathematical Notes 2 Theoretical and Mathematical Physics 2 Illinois Journal of Mathematics 2 Journal of Combinatorial Theory. Series A 2 Kyungpook Mathematical Journal 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Semigroup Forum 2 Tokyo Journal of Mathematics 2 Transactions of the Moscow Mathematical Society 2 Journal of Symbolic Computation 2 Bulletin of the American Mathematical Society. New Series 2 Expositiones Mathematicae 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 St. Petersburg Mathematical Journal 2 The New York Journal of Mathematics 2 Selecta Mathematica. New Series 2 Journal of the European Mathematical Society (JEMS) 2 Communications in Contemporary Mathematics 2 Journal of the Australian Mathematical Society 2 Mediterranean Journal of Mathematics 2 Journal of Homotopy and Related Structures 2 Journal of Topology and Analysis 2 Journal of $$K$$-Theory 2 Groups, Complexity, Cryptology 1 Discrete Applied Mathematics 1 Israel Journal of Mathematics 1 Letters in Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Mathematics of Computation 1 The Mathematical Intelligencer 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Compositio Mathematica 1 Demonstratio Mathematica 1 Duke Mathematical Journal 1 Fundamenta Mathematicae 1 Glasgow Mathematical Journal 1 Hiroshima Mathematical Journal 1 Journal of the London Mathematical Society. Second Series 1 Mathematika 1 Michigan Mathematical Journal 1 Pacific Journal of Mathematics 1 Proceedings of the Japan Academy. Series A 1 Theoretical Computer Science 1 Annals of Global Analysis and Geometry 1 Journal of the American Mathematical Society 1 MSCS. Mathematical Structures in Computer Science 1 Aequationes Mathematicae 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Archive for Mathematical Logic 1 Russian Mathematics 1 Journal of Algebraic Combinatorics 1 Applied Categorical Structures 1 The Electronic Journal of Combinatorics 1 Electronic Research Announcements of the American Mathematical Society 1 Documenta Mathematica 1 Doklady Mathematics 1 Representation Theory 1 Revista Matemática Complutense 1 New Journal of Physics 1 Annals of Mathematics. Second Series 1 Qualitative Theory of Dynamical Systems 1 JP Journal of Geometry and Topology 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Central European Journal of Mathematics 1 International Journal of Quantum Information 1 Foundations of Physics 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications ...and 12 more Serials
all top 5

#### Cited in 37 Fields

 458 Manifolds and cell complexes (57-XX) 190 Group theory and generalizations (20-XX) 74 Algebraic topology (55-XX) 39 Category theory; homological algebra (18-XX) 34 Associative rings and algebras (16-XX) 34 Nonassociative rings and algebras (17-XX) 24 Quantum theory (81-XX) 19 Order, lattices, ordered algebraic structures (06-XX) 18 Combinatorics (05-XX) 12 General algebraic systems (08-XX) 12 Differential geometry (53-XX) 8 Field theory and polynomials (12-XX) 7 Computer science (68-XX) 6 Mathematical logic and foundations (03-XX) 6 Global analysis, analysis on manifolds (58-XX) 5 General topology (54-XX) 4 Topological groups, Lie groups (22-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Convex and discrete geometry (52-XX) 3 General and overarching topics; collections (00-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Geometry (51-XX) 2 Algebraic geometry (14-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 $$K$$-theory (19-XX) 2 Fluid mechanics (76-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Information and communication theory, circuits (94-XX) 1 Number theory (11-XX) 1 Commutative algebra (13-XX) 1 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Abstract harmonic analysis (43-XX) 1 Functional analysis (46-XX) 1 Probability theory and stochastic processes (60-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX)