Volume 22, issue 1 (2022)

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

Volume 22, 1 issue

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
Asymptotic behavior of the colored Jones polynomials and Turaev–Viro invariants of the figure eight knot

Ka Ho Wong and Thomas Kwok-Keung Au

Algebraic & Geometric Topology 22 (2022) 1–53
Bibliography
1 J E Andersen, S K Hansen, Asymptotics of the quantum invariants for surgeries on the figure 8 knot, J. Knot Theory Ramifications 15 (2006) 479 MR2221531
2 Q Chen, T Yang, Volume conjectures for the Reshetikhin–Turaev and the Turaev–Viro invariants, Quantum Topol. 9 (2018) 419 MR3827806
3 R Detcherry, E Kalfagianni, T Yang, Turaev–Viro invariants, colored Jones polynomials, and volume, Quantum Topol. 9 (2018) 775 MR3874003
4 S Garoufalidis, Applications of quantum invariants in low-dimensional topology, Topology 37 (1998) 219 MR1480887
5 R M Kashaev, The hyperbolic volume of knots from the quantum dilogarithm, Lett. Math. Phys. 39 (1997) 269 MR1434238
6 H Murakami, The colored Jones polynomials of the figure-eight knot and the volumes of three-manifolds obtained by Dehn surgeries, Fund. Math. 184 (2004) 269 MR2128053
7 H Murakami, Some limits of the colored Jones polynomials of the figure-eight knot, Kyungpook Math. J. 44 (2004) 369 MR2095421
8 H Murakami, An introduction to the volume conjecture, from: "Interactions between hyperbolic geometry, quantum topology and number theory" (editors A Champanerkar, O Dasbach, E Kalfagianni, I Kofman, W Neumann, N Stoltzfus), Contemp. Math. 541, Amer. Math. Soc. (2011) 1 MR2796626
9 H Murakami, The coloured Jones polynomial, the Chern–Simons invariant, and the Reidemeister torsion of the figure-eight knot, J. Topol. 6 (2013) 193 MR3029425
10 H Murakami, J Murakami, The colored Jones polynomials and the simplicial volume of a knot, Acta Math. 186 (2001) 85 MR1828373
11 T Ohtsuki, On the asymptotic expansion of the Kashaev invariant of the 52 knot, Quantum Topol. 7 (2016) 669 MR3593566
12 W P Thurston, The geometry and topology of three-manifolds, lecture notes (1979)
13 K H Wong, T K K Au, Asymptotic behavior of colored HOMFLY polynomial of figure eight knot, preprint (2017) arXiv:1711.04437