## Experimental Mathematics

### Kashaev's Conjecture and the Chern-Simons Invariants of Knots and Links

#### Abstract

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.

#### Article information

Source
Experiment. Math., Volume 11, Issue 3 (2002), 427-435.

Dates
First available in Project Euclid: 9 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1057777432

Mathematical Reviews number (MathSciNet)
MR1959752

Zentralblatt MATH identifier
1117.57300

#### Citation

Murakami, Hitoshi; Murakami, Jun; Okamoto, Miyuki; Takata, Toshie; Yokota, Yoshiyuki. Kashaev's Conjecture and the Chern-Simons Invariants of Knots and Links. Experiment. Math. 11 (2002), no. 3, 427--435. https://projecteuclid.org/euclid.em/1057777432