Kashaev's conjecture and the Chern-Simons invariants of knots and links

Details Kashaev's conjecture and the Chern-Simons invariants of knots and links Kashaev's conjecture and the Chern-Simons invariants of knots and links

2002-03-13

arxiv.org/abs/math/0203119v2

Experiment. Math. 11 (2002), no. 3, 427--435

Mathematics

Geometric Topology

14 pages, 9 figures. Added some calculations

Scientific paper

R.M. Kashaev conjectured that the asymptotic behavior of his link invariant, 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 $6_3$, $8_9$ 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.

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