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

Volume 23
Issue 9, 3909–4400
Issue 8, 3417–3908
Issue 7, 2925–3415
Issue 6, 2415–2924
Issue 5, 1935–2414
Issue 4, 1463–1934
Issue 3, 963–1462
Issue 2, 509–962
Issue 1, 1–508

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
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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