Kashaev's Conjecture and the Chern-Simons Invariants of Knots and Links
Murakami, Hitoshi ; Murakami, Jun ; Okamoto, Miyuki ; Takata, Toshie ; Yokota, Yoshiyuki
Experiment. Math., Tome 11 (2002) no. 3, p. 427-435 / Harvested from Project Euclid
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R. M. Kashaev conjectured that the asymptotic behavior of the link invariant he introduced, which equals the colored Jones polynomial evaluated at a root of unity, determines the hyperbolic volume of any hyperbolic link complement. We observe numerically that for knots {\small $6_3$, $8_9$ and $8_{20}$} and for the Whitehead link, the colored Jones polynomials are related to the hyperbolic volumes and the Chern--Simons invariants and propose a complexification of Kashaev's conjecture.
Publié le : 2002-05-14
Classification:  Volume conjecture,  Kashaev's conjecture,  colored Jones polynomial,  Chern-Simons invariant,  volume,  57M27,  57M25,  57M50,  41A60,  17B37,  81R50 
@article{1057777432,
     author = {Murakami, Hitoshi and Murakami, Jun and Okamoto, Miyuki and Takata, Toshie and Yokota, Yoshiyuki},
     title = {Kashaev's Conjecture and the Chern-Simons Invariants of Knots and Links},
     journal = {Experiment. Math.},
     volume = {11},
     number = {3},
     year = {2002},
     pages = { 427-435},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1057777432}
}

Murakami, Hitoshi; Murakami, Jun; Okamoto, Miyuki; Takata, Toshie; Yokota, Yoshiyuki. Kashaev's Conjecture and the Chern-Simons Invariants of Knots and Links. Experiment. Math., Tome 11 (2002) no. 3, pp.  427-435. http://gdmltest.u-ga.fr/item/1057777432/