Download this article
 Download this article For screen
For printing
Recent Issues

Volume 25, 1 issue

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
A quantum invariant of links in $T^2 \times I$ with volume conjecture behavior

Joe Boninger

Algebraic & Geometric Topology 23 (2023) 1891–1934
Bibliography
1 C Adams, O Eisenberg, J Greenberg, K Kapoor, Z Liang, K O’Connor, N Pacheco-Tallaj, Y Wang, tg–hyperbolicity of virtual links, J. Knot Theory Ramifications 28 (2019) 1950080 MR4059928
2 J S Carter, S Kamada, M Saito, Stable equivalence of knots on surfaces and virtual knot cobordisms, J. Knot Theory Ramifications 11 (2002) 311 MR1905687
3 A Champanerkar, I Kofman, J S Purcell, Geometrically and diagrammatically maximal knots, J. Lond. Math. Soc. 94 (2016) 883 MR3614933
4 A Champanerkar, I Kofman, J S Purcell, Geometry of biperiodic alternating links, J. Lond. Math. Soc. 99 (2019) 807 MR3977891
5 Q Chen, T Yang, Volume conjectures for the Reshetikhin–Turaev and the Turaev–Viro invariants, Quantum Topol. 9 (2018) 419 MR3827806
6 F Costantino, Coloured Jones invariants of links and the volume conjecture, J. Lond. Math. Soc. 76 (2007) 1 MR2351605
7 R Detcherry, E Kalfagianni, T Yang, Turaev–Viro invariants, colored Jones polynomials, and volume, Quantum Topol. 9 (2018) 775 MR3874003
8 P J Freyd, D N Yetter, Braided compact closed categories with applications to low-dimensional topology, Adv. Math. 77 (1989) 156 MR1020583
9 S Garoufalidis, T T Q Lê, Asymptotics of the colored Jones function of a knot, Geom. Topol. 15 (2011) 2135 MR2860990
10 J Green, A table of virtual knots, electronic resource (2004)
11 S A Grishanov, V R Meshkov, A V Omelchenko, Kauffman-type polynomial invariants for doubly periodic structures, J. Knot Theory Ramifications 16 (2007) 779 MR2341317
12 R M Kashaev, The hyperbolic volume of knots from the quantum dilogarithm, Lett. Math. Phys. 39 (1997) 269 MR1434238
13 C Kassel, Quantum groups, 155, Springer (1995) MR1321145
14 L H Kauffman, State models and the Jones polynomial, Topology 26 (1987) 395 MR899057
15 L H Kauffman, Virtual knot theory, European J. Combin. 20 (1999) 663 MR1721925
16 L H Kauffman, Rotational virtual knots and quantum link invariants, J. Knot Theory Ramifications 24 (2015) 1541008 MR3434547
17 R Kirby, P Melvin, The 3–manifold invariants of Witten and Reshetikhin–Turaev for sl(2,C), Invent. Math. 105 (1991) 473 MR1117149
18 A N Kirillov, N Y Reshetikhin, Representations of the algebra Uq(sl(2)), q–orthogonal polynomials and invariants of links, from: "Infinite-dimensional Lie algebras and groups" (editor V G Kac), Adv. Ser. Math. Phys. 7, World Sci. (1989) 285 MR1026957
19 V Krushkal, Graphs, links, and duality on surfaces, Combin. Probab. Comput. 20 (2011) 267 MR2769192
20 G Kuperberg, What is a virtual link?, Algebr. Geom. Topol. 3 (2003) 587 MR1997331
21 X S Lin, Z Wang, Random walk on knot diagrams, colored Jones polynomial and Ihara–Selberg zeta function, from: "Knots, braids, and mapping class groups — papers dedicated to Joan S. Birman" (editors J Gilman, W W Menasco, X S Lin), AMS/IP Stud. Adv. Math. 24, Amer. Math. Soc. (2001) 107 MR1873112
22 H R Morton, Invariants of links and 3–manifolds from skein theory and from quantum groups, from: "Topics in knot theory" (editor M E Bozhüyük), NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 399, Kluwer Acad. (1993) 107 MR1257908
23 H R Morton, P Strickland, Jones polynomial invariants for knots and satellites, Math. Proc. Cambridge Philos. Soc. 109 (1991) 83 MR1075123
24 H Murakami, J Murakami, The colored Jones polynomials and the simplicial volume of a knot, Acta Math. 186 (2001) 85 MR1828373
25 H Murakami, Y Yokota, Volume conjecture for knots, 30, Springer (2018) MR3837111
26 T Ohtsuki, On the asymptotic expansion of the quantum SU(2) invariant at q = exp(4π√−-1∕N) for closed hyperbolic 3–manifolds obtained by integral surgery along the figure-eight knot, Algebr. Geom. Topol. 18 (2018) 4187 MR3892244
27 J H Przytycki, Skein modules of 3–manifolds, Bull. Polish Acad. Sci. Math. 39 (1991) 91 MR1194712
28 N Y Reshetikhin, V G Turaev, Ribbon graphs and their invariants derived from quantum groups, Comm. Math. Phys. 127 (1990) 1 MR1036112
29 T Soma, The Gromov invariant of links, Invent. Math. 64 (1981) 445 MR632984
30 V G Turaev, The Conway and Kauffman modules of a solid torus, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 167 (1988) 79, 190 MR964255
31 V G Turaev, The Yang–Baxter equation and invariants of links, Invent. Math. 92 (1988) 527 MR939474
32 V G Turaev, Quantum invariants of knots and 3–manifolds, 18, de Gruyter (1994) MR1292673
33 R van der Veen, Proof of the volume conjecture for Whitehead chains, Acta Math. Vietnam. 33 (2008) 421 MR2501851
34 R van der Veen, The volume conjecture for augmented knotted trivalent graphs, Algebr. Geom. Topol. 9 (2009) 691 MR2496886