[1] Chen, Q., Yang, T., Volume conjectures for the Reshetikhin-Turaev and the Turaev-Viro invariants,
Quantum Topol. 9 (2018) 419–460.
[2] Dimofte, T., Gaiotto, D., Gukov, S., 3-manifolds and 3d indices, Adv. Theor. Math. Phys. 17 (2013)
975–1076.
[3] Garoufalidis, S., The 3D index of an ideal triangulation and angle structures. With an appendix by
Sander Zwegers, Ramanujan J. 40 (2016) 573–604.
[4] Garoufalidis, S., Hodgson, C. D., Hoffman, N. R., Rubinstein, J. H., The 3D-index and normal
surfaces, Illinois J. Math. 60 (2016) 289–352.
[5] Garoufalidis, S., Hodgson, C. D., Rubinstein, J. H., Segerman, H., 1-efficient triangulations and the
index of a cusped hyperbolic 3-manifold, Geom. Topol. 19 (2015) 2619–2689.
[6] Garoufalidis, S., Kashaev, R., A meromorphic extension of the 3D index, Res. Math. Sci. 6 (2019)
Paper No. 8, 34 pp.
75
[7] Garoufalidis, S., Vuong, T., A stability conjecture for the colored Jones polynomial, Topology Proc.
49 (2017) 211–249.
[8] Garoufalidis, S., Wheeler, C., Periods, the meromorphic 3D-index and the Turaev–Viro invariant,
arXiv:2209.02843.
[9] Garoufalidis, S., Yoon, S., Twisted Neumann–Zagier matrices, arXiv:2109.00379.
[10] Garoufalidis, S., Yoon, S., Asymptotically multiplicative quantum invariants, arXiv:2211.00270.
[11] Kashaev, R.M., The hyperbolic volume of knots from the quantum dilogarithm, Lett. Math. Phys. 39
(1997) 269–275.
[12] Hodgson, C. D., Kricker, A. J., Siejakowski, R. M., On the asymptotics of the meromorphic 3D-index,
arXiv:2109.05355.
[13] Murakami, H., Murakami, J., The colored Jones polynomials and the simplicial volume of a knot,
Acta Math. 186 (2001) 85–104.
[14] Neumann, W. D., Combinatorics of triangulations and the Chern-Simons invariant for hyperbolic
3-manifolds, Topology ’90 (Columbus, OH, 1990), 243–271, Ohio State Univ. Math. Res. Inst. Publ.
1, de Gruyter, Berlin, 1992.
[15] Neumann, W. D., Zagier, D., Volumes of hyperbolic three-manifolds, Topology 24 (1985) 307–332.
[16] Ohtsuki, T., On the asymptotic expansion of the Kashaev invariant of the 52 knot, Quantum Topol.
7 (2016) 669–735.
[17] Ohtsuki, T., On the asymptotic expansion of the Kashaev invariant of the knots with seven crossings,
Internat. J. Math. 28 (2017), no. 13, 1750096, 143 pp.
[18] Ohtsuki, T., 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) 4187–4274.
[19] Ohtsuki, T., Yokota, Y., On the asymptotic expansion of the Kashaev invariant of the knots with 6
crossings, Math. Proc. Cambridge Philos. Soc. 165 (2018) 287–339.
[20] Thurston, W. P., The geometry and topology of three-manifolds, the 1980 lecture notes at Princeton
University, http://library.msri.org/books/gt3m/
[21] Thurston, D.P., Hyperbolic volume and the Jones polynomial, Notes accompanying lectures at
the summer school on quantum invariants of knots and three-manifolds, Joseph Fourier Institute, University of Grenoble, org. C. Lescop, July, 1999. https://dpthurst.pages.iu.edu/
speaking/Grenoble.pdf
[22] Yokota, Y., On the volume conjecture for hyperbolic knots, arXiv:math/ 0009165.
[23] Yokota, Y., On the complex volume of hyperbolic knots, J. Knot Theory Ramifications 20 (2011)
955–976.
Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan
E-mail address: tomotada@kurims.kyoto-u.ac.jp
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