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Distinguishing mutant knots. (English) Zbl 07299385
Summary: Knot theory is actively studied both by physicists and mathematicians as it provides a connecting centerpiece for many physical and mathematical theories. One of the challenging problems in knot theory is distinguishing mutant knots. Mutant knots are not distinguished by colored HOMFLY-PT polynomials for knots colored by either symmetric and or antisymmetric representations of \(SU(N)\). Some of the mutant knots can be distinguished by the simplest non-symmetric representation \([2,1 ]\). However there is a class of mutant knots which require more complex representations like \([4,2]\). In this paper we calculate polynomials and differences for the mutant knot polynomials in representations \([3,1]\) and \([4,2]\) and study their properties.
MSC:
57K10 Knot theory
57K16 Finite-type and quantum invariants, topological quantum field theories (TQFT)
57K14 Knot polynomials
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[1] Akutsu, Y.; Deguchi, T.; Ohtsuki, T., Invariants of colored links, J. Knot Theory Ramifications, 1, 161 (1992) · Zbl 0758.57004
[2] Akutsu, Y.; Wadati, M., Knots, links, braids and exactly solvable models in statistical mechanics, Comm. Math. Phys., 117, 243 (1988) · Zbl 0651.57005
[3] V. Alekseev, An. Morozov, A. Sleptsov, Interplay between symmetries of quantum 6-j symbols and the eigenvalue hypothesis, arXiv:1909.07601.
[4] Alekseev, V., Multiplicity-free \(U_q ( s l_N ) 6\)-j symbols: relations, asymptotics, symmetries, Nuclear Phys. B (2020)
[5] Amburg, N.; Orlov, A.; Vasiliev, D., On products of random matrices, Entropy, 22.9:972 (2020)
[6] A. Anokhina, On R-matrix approaches to knot invariants, arXiv:1412.8444. · Zbl 1407.81006
[7] Anokhina, A.; Mironov, A.; Morozov, A.; Morozov, An., Colored HOMFLY polynomials as multiple sums over paths or standard Young tableaux, Adv. High Energy Phys., 2013, Article 931830 pp. (2013), arXiv:1304.1486 · Zbl 1328.81123
[8] Anokhina, A.; Mironov, A.; Morozov, A.; Morozov, An., Racah coefficients and extended HOMFLY polynomials for all 5-, 6- and 7-strand braids, Nuclear Phys., B868, 271-313 (2013), arXiv:1207.0279 · Zbl 1262.81073
[9] Anokhina, A.; Mironov, A.; Morozov, A.; Morozov, An., Knot polynomials in the first non-symmetric representation, Nuclear Phys. B, 882, 171-194 (2014), arXiv:1211.6375 · Zbl 1285.81035
[10] Anokhina, A.; Morozov, An., Cabling procedure for the colored HOMFLY polynomials, Theoret. Math. Phys., 178, 1-58 (2014), arXiv:1307.2216 · Zbl 1318.81055
[11] Anokhina, A.; Morozov, A.; Popolitov, A., Nimble evolution for pretzel Khovanov polynomials, Eur. Phys. J. C, 79, 867 (2019), arXiv:1904.10277
[12] Arthamonov, S.; Mironov, A.; Morozov, A., Differential hierarchy and additional grading of knot polynomials, Theoret. Math. Phys., 179, 509-542 (2014), arXiv:1306.5682 · Zbl 1333.57008
[13] Bai, C.; Jiang, J.; Liang, J.; Mironov, A.; Morozov, A.; Morozov, An.; Sleptsov, A., Differential expansion for link polynomials, Phys. Lett. B, 778, 197-206 (2018), arXiv:1709.09228 · Zbl 1383.57002
[14] Bai, C.; Jiang, J.; Liang, J.; Mironov, A.; Morozov, A.; Morozov, An.; Sleptsov, A., Quantum Racah matrices up to level 3 and multicolored link invariants, J. Geom. Phys., 132, 155-180 (2018), arXiv:1801.09363 · Zbl 1397.57023
[15] Balasubramanian, V.; DeCross, M.; Fliss, J.; Kar, A.; Leigh, R. G.; Parrikar, O., Entanglement entropy and the colored Jones polynomial, J. High Energy Phys., 1805, 038 (2018), arXiv:1801.01131
[16] Balasubramanian, V.; Fliss, J. R.; Leigh, R. G.; Parrikar, O., Multi-boundary entanglement in Chern-Simons theory and link invariants, J. High Energy Phys., 1704, 061 (2017), arXiv:1611.05460 · Zbl 1378.81061
[17] D. Bar-Natan, S. Morrison, http://katlas.org.
[18] Bishler, L.; Dhara, Saswati; Grigoryev, T.; Mironov, A.; Morozov, A.; Morozov, An.; Ramadevi, P.; Singh, Vivek Kumar; Sleptsov, A., Difference of mutant knot invariants and their differential expansion, Pis’ma Zh. Eksp. Teor. Fiz., 111, 591 (2020), arXiv:2004.06598
[19] L. Bishler, A. Morozov, Perspectives of differential expansion of colored knot polynomials, arXiv:2006.01190.
[20] Bishler, L.; Morozov, An.; Sleptsov, A.; Shakirov, Sh., On the block structure of the quantum R-matrix in the three-strand braids, Internat. J. Modern Phys. A, 33, Article 1850105 pp. (2018), arXiv:1712.07034 · Zbl 1392.81203
[21] Bonahon, F.; Siebenmann, L. C., New geometric splittings of classical knots and the classification and symmetries of arborescent knots (2010), http://www-bcf.usc.edu/ fbonahon/Research/Preprints/BonSieb.pdf
[22] Brini, A.; Eynard, B.; Marino, M., Torus knots and mirror symmetry, Ann. Henri Poincaré, 13, 1873 (2012), arXiv:1105.2012 · Zbl 1256.81086
[23] Caudron, A., Classification des Noeuds et des Enlacements, Publ. Math. Orsay 82-4 (1982), University of Paris XI: University of Paris XI Orsay
[24] Chern, S.-S.; Simons, J., Characteristic forms and geometric invariants, Ann. of Math., 99, 48-69 (1974) · Zbl 0283.53036
[25] Conway, J. H., An enumeration of knots and links, and some of their algebraic properties, (Leech, John, Computational Problems in Abstract Algebra, Proc. Conf. Oxford, 1967 (1970), Pergamon Press: Pergamon Press Oxford-New York), 329-358
[26] D. De Wit, J. Links, Where the Links-Gould invariant first fails to distinguish nonmutant prime knots, math/0501224. · Zbl 1187.57013
[27] Dhara, S.; Mironov, A.; Morozov, A.; Morozov, An.; Ramadevi, P.; Singh, Vivek Kumar; Sleptsov, A., Multi-colored links from 3-strand braids carrying arbitrary symmetric representations, Ann. Henri Poincaré, 20, 12, 4033-4054 (2019), arXiv:1805.03916 · Zbl 1426.81044
[28] Dunfield, N. M.; Gukov, S.; Rasmussen, J., The superpolynomial for knot homologies, Exp. Math., 15, 129-159 (2006), math/0505662 · Zbl 1118.57012
[29] Dunin-Barkowski, P.; Mironov, A.; Morozov, A.; Sleptsov, A.; Smirnov, A., Superpolynomials for toric knots from evolution induced by cut-and-join operators, J. High Energy Phys., 1303, 021 (2013), arXiv:1106.4305 · Zbl 1342.57004
[30] Dunin-Barkowski, P.; Popolitov, A.; Shadrin, S.; Sleptsov, A., Combinatorial structure of colored HOMFLY-PT polynomials for torus knots, Commun. Number Theory Phys., 13, 763 (2019), arXiv:1712.08614 · Zbl 1429.81080
[31] Dwivedi, S.; Singh, V. K.; Dhara, S.; Ramadevi, P.; Zhou, Y.; Joshi, L. K., Entanglement on linked boundaries in Chern-Simons theory with generic gauge groups, J. High Energy Phys., 1802, 163 (2018), arXiv:1711.06474 · Zbl 1387.58029
[32] Dwivedi, S.; Singh, V. K.; Ramadevi, P.; Zhou, Y.; Dhara, S., Entanglement on multiple \(S^2\) boundaries in Chern-Simons theory, J. High Energy Phys., 1908, 034 (2019), arXiv:1906.11489
[33] S. Dwivedi, V.K. Singh, A. Roy, Semiclassical limit of topological Rényi entropy in \(3 d\) Chern-Simons theory, arXiv:2007.07033.
[34] Freyd, P.; Yetter, D.; Hoste, J.; Lickorish, W. B.R.; Millett, K.; Ocneanu, A., A new polynomial invariant of knots and links, Am. Math. Soc., 12, 239-246 (1985) · Zbl 0572.57002
[35] Galakhov, D.; Melnikov, D.; Mironov, A.; Morozov, A.; Sleptsov, A., Colored knot polynomials for Pretzel knots and links of arbitrary genus, Phys. Lett. B, 743, 71-74 (2015), arXiv:1412.2616 · Zbl 1343.57007
[36] R. Gopakumar, C. Vafa, M Theory and Topological Strings. 2, arXiv:hep-th/9812127.
[37] Gopakumar, R.; Vafa, C., On the gauge theory/geometry correspondence, AMS/IP Stud. Adv. Math., 23, 45-63 (2001), arXiv:hep-th/9811131 · Zbl 1026.81029
[38] E. Gorsky, S. Gukov, M. Stosic, Quadruply-graded colored homology of knots, arXiv:1304.3481. · Zbl 1432.57026
[39] Gu, J.; Jockers, H., A note on colored HOMFLY polynomials for hyperbolic knots from WZW models, Comm. Math. Phys., 338, 393-456 (2015), arXiv:1407.5643 · Zbl 1328.81193
[40] Guadagnini, E.; Martellini, M.; Mintchev, M., Phys. Lett., B235, 275 (1990)
[41] E. Guadagnini, M. Mintchev, M. Martellini, Chern-Simons field theory and quantum groups, In: Clausthal 1989, Proceedings, Quantum Groups, 307-317. · Zbl 0722.57003
[42] Gukov, S.; Nawata, S.; Saberi, I.; Stosic, M.; Sulkowski, P., Sequencing BPS spectra, J. High Energy Phys., 1603, 004 (2016), arXiv:1512.07883 · Zbl 1388.81823
[43] Gukov, S.; Stošić, M., Homological algebra of knots and BPS states, Proc. Sympos. Pure Math.. Proc. Sympos. Pure Math., Geom. Topol. Monographs, 18, 2012, 309 (2012) · Zbl 1296.57014
[44] http://knotebook.org.
[45] Itoyama, H.; Mironov, A.; Morozov, A.; Morozov, An., Character expansion for HOMFLY polynomials. III. All 3-strand braids in the first symmetric representation, Internat. J. Modern Phys., A27, Article 1250099 pp. (2012), arXiv:1204.4785 · Zbl 1260.81134
[46] Itoyama, H.; Mironov, A.; Morozov, A.; Morozov, A., HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations, J. High Energy Phys., 1207, 131 (2012), arXiv:1203.5978 · Zbl 1397.57012
[47] Itoyama, H.; Mironov, A.; Morozov, A.; Morozov, An., Eigenvalue hypothesis for Racah matrices and HOMFLY polynomials for 3-strand knots in any symmetric and antisymmetric representations, Internat. J. Modern Phys. A, 28, Article 1340009 pp. (2013), arXiv:1209.6304 · Zbl 1259.81082
[48] M. Kameyama, S. Nawata, R. Tao, H.D. Zhang, Cyclotomic expansions of HOMFLY-PT colored by rectangular Young diagrams, arXiv:1902.02275.
[49] L.H. Kauffman, Knot logic and topological quantum computing with majorana fermions, arXiv:1301.6214. · Zbl 1355.81059
[50] Kaul, R. K.; Govindarajan, T. R., Three dimensional Chern-Simons theory as a theory of knots and links, Nuclear Phys. B, 380, 293-336 (1992), arXiv:hep-th/9111063 · Zbl 0938.81553
[51] Klimyk, A.; Schmüdgen, K., Quantum Groups and their Representations (2012), Springer Science & Business Media
[52] Kolganov, N.; Morozov, An., Quantum R-matrices as universal qubit gates, JETP Lett., 111, 519-524 (2020), arXiv:2004.07764
[53] Kononov, Ya.; Morozov, A., On the defect and stability of differential expansion, JETP Lett., 101, 831-834 (2015), arXiv:1504.07146
[54] J.M.F. Labastida, M. Marino, A New point of view in the theory of knot and link invariants, math/0104180. · Zbl 1002.57026
[55] Labastida, J. M.F.; Marino, M., Polynomial invariants for torus knots and topological strings, Comm. Math. Phys., 217, 423 (2001), hep-th/0004196 · Zbl 1018.81049
[56] Labastida, J. M.F.; Marino, M.; Vafa, C., Knots, links and branes at large N, J. High Energy Phys., 0011, 007 (2000), hep-th/0010102 · Zbl 0990.81545
[57] Lin, X.-S.; Zheng, H., On the Hecke algebras and the colored HOMFLY polynomial, Trans. Amer. Math. Soc., 362, 1-18 (2010), math/0601267 · Zbl 1193.57006
[58] Mariño, M., String theory and the Kauffman polynomial, Comm. Math. Phys., 298, 613 (2010), arXiv:0904.1088 · Zbl 1207.81129
[59] Marino, M.; Vafa, C., Framed knots at large N, Contemp. Math., 310, 185 (2002), hep-th/0108064 · Zbl 1042.81071
[60] Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An., Towards topological quantum computer, Nuclear Phys. B, 926, 491-508 (2018), arXiv:1703.00431 · Zbl 1380.81088
[61] Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An., From topological to quantum entanglement, J. High Energy Phys., 2005, 116 (2019), arXiv:1809.04574 · Zbl 1416.81170
[62] Mironov, S., Topological entanglement and knots, Universe, 5, 60 (2019)
[63] Mironov, A.; Mironov, S.; Mishnyakov, V.; Morozov, A.; Sleptsov, A., Coloured Alexander polynomials and KP hierarchy, Phys. Lett. B, 783, 268 (2018), arXiv:1805.02761 · Zbl 1414.37030
[64] Mironov, A.; Mkrtchyan, R.; Morozov, A., On universal knot polynomials, J. High Energy Phys., 02, 78 (2016), arXiv:1510.05884 · Zbl 1388.81174
[65] Mironov, A.; Morozov, A., Towards effective topological field theory for knots, Nuclear Phys. B, 899, 395-413 (2015), arXiv:1506.00339 · Zbl 1331.81264
[66] Mironov, A.; Morozov, A., Universal Racah matrices and adjoint knot polynomials. I. Arborescent knots, Phys. Lett., B755, 47-57 (2016), arXiv:1511.09077 · Zbl 1367.81090
[67] Mironov, A.; Morozov, A., Eigenvalue conjecture and colored Alexander polynomials, Eur. Phys. J. C, 78, 284 (2018), arXiv:1610.03043
[68] Mironov, A.; Morozov, A.; Morozov, An., Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid, J. High Energy Phys., 03, 034 (2012), arXiv:1112.2654 · Zbl 1309.81114
[69] Mironov, A.; Morozov, A.; Morozov, An., Character expansion for HOMFLY polynomials. I. Integrability and difference equations, (Rebhan, A.; Katzarkov, L.; Knapp, J.; Rashkov, R.; Scheidegger, E., Strings, Gauge Fields, and the Geometry behind: The Legacy of Maximilian Kreuzer (2013), World Scietific Publishins Co.Pte.Ltd), 101-118, arXiv:1112.5754
[70] Mironov, A.; Morozov, A.; Morozov, An., Evolution method and “differential hierarchy” of colored knot polynomials, AIP Conf. Proc., 1562, 1 (2013), 123-155, arXiv:1306.3197
[71] Mironov, A.; Morozov, A.; Morozov, An., On colored HOMFLY polynomials for twist knots, Modern Phys. Lett. A, 29, Article 1450183 pp. (2014), arXiv:1408.3076 · Zbl 1302.81134
[72] Mironov, A.; Morozov, A.; Morozov, An.; Ramadevi, P.; Singh, Vivek Kumar, Colored HOMFLY polynomials of knots presented as double fat diagrams, J. High Energy Phys., 1507, 109 (2015), arXiv:1504.00371 · Zbl 1388.57010
[73] Mironov, A.; Morozov, A.; Morozov, A.; Ramadevi, P.; Singh, V. K.; Sleptsov, A., Checks of integrality properties in topological strings, J. High Energy Phys.. J. High Energy Phys., J. High Energy Phys., 1801, 143 (2018), Addendum; arXiv:1702.06316
[74] Mironov, A.; Morozov, A.; Morozov, An.; Ramadevi, P.; Singh, Vivek Kumar; Sleptsov, A., Tabulating knot polynomials for arborescent knots, J. Phys. A, 50, Article 085201 pp. (2017), arXiv:1601.04199 · Zbl 1360.81271
[75] Mironov, A.; Morozov, A.; Morozov, An.; Sleptsov, A., Colored knot polynomials. HOMFLY in representation [2, 1], J. Mod. Phys., A30, Article 1550169 pp. (2015), arXiv:1508.02870 · Zbl 1333.81202
[76] Mironov, A.; Morozov, A.; Morozov, An.; Sleptsov, A., HOMFLY polynomials in representation [3, 1] for 3-strand braids, J. High Energy Phys., 2016, 134 (2016), arXiv:1605.02313 · Zbl 1388.57011
[77] Mironov, A.; Morozov, A.; Morozov, An.; Sleptsov, A., Quantum Racah matrices and 3-strand braids in irreps R with \(| R | = 4\), JETP Lett., 104, 56-61 (2016), arXiv:1605.03098
[78] Mironov, A.; Morozov, A.; Morozov, An.; Sleptsov, A., Racah matrices and hidden integrability in evolution of knots, Phys. Lett. B, 760, 45-58 (2016), arXiv:1605.04881 · Zbl 1398.57025
[79] Mironov, A.; Morozov, A.; Natanzon, S., Complete set of cut-and-join operators in Hurwitz-Kontsevich theory, Theoret. Math. Phys., 166, 1 (2011), arXiv:0904.4227 · Zbl 1312.81125
[80] Mironov, A.; Morozov, A.; Natanzon, S., Algebra of differential operators associated with Young diagrams, J. Geom. Phys., 62, 148 (2012), arXiv:1012.0433 · Zbl 1242.22008
[81] Mironov, A.; Morozov, A.; Sleptsov, A., Genus expansion of HOMFLY polynomials, Theoret. Math. Phys., 177, 179-221 (2013), arXiv:1303.1015 · Zbl 1336.57022
[82] Mironov, A.; Morozov, A.; Sleptsov, A., On genus expansion of knot polynomials and hidden structure of Hurwitz tau-functions, Eur. Phys. J. C, 73, 2492 (2013), arXiv:1304.7499
[83] Mironov, A.; Morozov, A.; Sleptsov, A., Colored HOMFLY polynomials for the pretzel knots and links, J. High Energy Phys., 1507, 069 (2015), arXiv:1412.8432 · Zbl 1388.57012
[84] Mironov, A.; Morozov, A.; Sleptsov, A.; Smirnov, A., On genus expansion of superpolynomials, Nuclear Phys. B, 889, 757 (2014), arXiv:1310.7622 · Zbl 1326.57030
[85] V. Mishnyakov, A. Sleptsov, Perturbative analysis of the colored Alexander polynomial and KP soliton \(\tau \)-functions, arXiv:1906.05813.
[86] V. Mishnyakov, A. Sleptsov, N. Tselousov, A new symmetry of the colored Alexander polynomial, arXiv:2001.10596.
[87] V. Mishnyakov, A. Sleptsov, N. Tselousov, A novel symmetry of colored HOMFLY polynomials coming from \(\mathfrak{sl} ( N | M )\) superalgebras, arXiv:2005.01188.
[88] A. Morozov, Extension of KNTZ trick to non-rectangular representations, arXiv:1903.00259. · Zbl 1420.57027
[89] Morozov, A., Differential expansion and rectangular HOMFLY for the figure eight knot, Nuclear Phys. B, 911, 582-605 (2016), arXiv:1605.09728 · Zbl 1346.81079
[90] Morozov, A., Factorization of differential expansion for antiparallel double-braid knots, J. High Energy Phys., 1609, 135 (2016), arXiv:1606.06015 · Zbl 1388.57013
[91] Morozov, A., On moduli space of symmetric orthogonal matrices and exclusive Racah matrix \(\overline{S}\) for representation \(R = [ 3 , 1 ]\) with multiplicities, Phys. Lett., B766, 291-300 (2017), arXiv:1701.00359 · Zbl 1397.81091
[92] Morozov, A., Factorization of differential expansion for non-rectangular representations, Modern Phys. Lett. A, 33, Article 1850062 pp. (2018), arXiv:1612.00422 · Zbl 1386.81097
[93] Morozov, A.; Smirnov, A., Chern-Simons theory in the temporal gauge and knot invariants through the universal quantum R-matrix, Nuclear Phys. B, 835, 284-313 (2010), arXiv:1001.2003 · Zbl 1204.81097
[94] Morton, H. R., Mutant knots with symmetry, Math. Proc. Camb. Phil. Soc., 146, 95-107 (2009), arXiv:0705.1321 · Zbl 1169.57010
[95] Morton, H. R.; Ryder, H. J., Mutants and \(S U ( 3 )_q\) invariants, Geom. Topol. Monogr., 1, 365-381 (1998), math/9810197 · Zbl 0901.57002
[96] Nawata, S.; Ramadevi, P.; Singh, Vivek Kumar, Colored HOMFLY polynomials that distinguish mutant knots, J. Knot Theory Ramifications, 26, Article 1750096 pp. (2017), arXiv:1504.00364 · Zbl 1405.57017
[97] Nawata, S.; Ramadevi, P.; Zodinmawia, Vivek Kumar, Colored HOMFLY polynomials from Chern-Simons theory, J. Knot Theory Ramifications, 22, 13 (2013), arXiv:1302.5144 · Zbl 1296.57015
[98] Ooguri, H.; Vafa, C., Knot invariants and topological strings, Nuclear Phys. B, 577, 419-438 (2000), arXiv:hep-th/9912123 · Zbl 1036.81515
[99] Paul, C.; Borhade, P.; Ramadevi, P., Composite representation invariants and unoriented topological string amplitudes, Nuclear Phys. B, 841, 448-462 (2010), arXiv:1008.3453 · Zbl 1207.81077
[100] Przytycki, J. H.; Traczyk, P., Invariants of links of conway type, Kobe J. Math., 4, 115-139 (1987), arXiv:1610.06679 · Zbl 0655.57002
[101] Ramadevi, P.; Govindarajan, T. R.; Kaul, R. K., Three dimensional Chern-Simons theory as a theory of knots and links III : Compact semi-simple group, Nuclear Phys. B, 402, 548-566 (1993), arXiv:hep-th/9212110 · Zbl 0941.57500
[102] Ramadevi, P.; Govindarajan, T. R.; Kaul, R. K., Chirality of knots \(9_{42}\) and \(1 0_{71}\) and Chern-Simons theory, Modern Phys. Lett. A, 9, 3205-3218 (1994), hep-th/9401095 · Zbl 1015.57500
[103] Ramadevi, P.; Govindarajan, T. R.; Kaul, R. K., Knot invariants from rational conformal field theories, Nuclear Phys. B, 422, 291-306 (1994), arXiv:hep-th/9312215 · Zbl 0990.81694
[104] Ramadevi, P.; Sarkar, T., On link invariants and topological string amplitudes, Nuclear Phys. B, 600, 487-511 (2001), hep-th/0009188 · Zbl 1097.81742
[105] N.Yu. Reshetikhin, Quantized universal envelopment algebras, the Yang-Baxter equation and invariants of links. I, LOMI preprint E-4-87, https://math.berkeley.edu/reshetik/Publications/QGInv-1-1987.pdf.
[106] N.Yu. Reshetikhin, Quantized universal envelopment algebras, the Yang-Baxter equation and invariants of links. II, LOMI E-17-87, https://math.berkeley.edu/reshetik/Publications/QGInv-2-1987.pdf.
[107] Reshetikhin, N. Yu.; Takhtadjan, L. A.; Faddeev, L. D., Quantization of Lie groups and Lie algebras, Algebra Anal., 1, 178-206 (1989)
[108] Reshetikhin, N. Yu.; Turaev, V. G., Chern-Simons theory in the temporal gauge and knot invariants through the universal quantum R-matrix, Comm. Math. Phys., 127, 1-26 (1990) · Zbl 0768.57003
[109] Reshetikhin, N.; Turaev, V. G., Invariants of three manifolds via link polynomials and quantum groups, Invent. Math., 103, 547-597 (1991) · Zbl 0725.57007
[110] Rosso, M.; Jones, V., On the invariants of torus knots derived from quantum groups, J. Knot Theory Ramifications, 2, 97-112 (1993) · Zbl 0787.57006
[111] Sh. Shakirov, A. Sleptsov, Quantum Racah matrices and 3-strand braids in representation [3, 3], arXiv:1611.03797.
[112] Smirnov, A., Notes on Chern-Simons theory in the temporal gauge, Subnucl. Ser., 47, 489-498 (2011), arXiv:0910.5011
[113] Stevan, S., Chern-Simons invariants of torus links, Ann. Henri Poincaré, 11, 1201-1224 (2010), arXiv:1003.2861 · Zbl 1208.81149
[114] Stevan, S., Torus knots in lens spaces and topological strings, Ann. Henri Poincaré, 16, 1937 (2015), arXiv:1308.5509 · Zbl 1321.81053
[115] Stoimenow, A., Tabulating and distinguishing mutants, Internat. J. Algebra Comput., 20, 525-559 (2010), http://http://stoimenov.net/stoimeno/homepage/ptab/index.html · Zbl 1195.57021
[116] Tierz, M., Soft matrix models and Chern-Simons partition functions, Modern Phys. Lett. A, 19, 1365-1378 (2004), hep-th/0212128 · Zbl 1076.81544
[117] Turaev, V. G., The Yang-Baxter equation and invariants of links, Invent. Math., 92, 527-553 (1988) · Zbl 0648.57003
[118] Turaev, V. G.; Viro, O. Y., State sum invariants of 3 manifolds and quantum 6j symbols, Topology, 31, 865 (1992) · Zbl 0779.57009
[119] Witten, E., Quantum field theory and the jones polynomial, Comm. Math. Phys., 121, 351-399 (1989) · Zbl 0667.57005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.