2002/03/31 by Hitoshi Murakami, Jun Murakami, Miyuki Okamoto +2 · 1 citation
Mathematics · #math.GT #msc:57M27
published as Experiment. Math. 11 (2002), no. 3, 427--435 · 14 pages, 9 figures. Added some calculations
arxiv created 2002/06/17 · arxiv updated 2009/11/30
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 63, 89 and 820 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.