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2002 Kashaev's Conjecture and the Chern-Simons Invariants of Knots and Links
Hitoshi Murakami, Jun Murakami, Miyuki Okamoto, Toshie Takata, Yoshiyuki Yokota
Experiment. Math. 11(3): 427-435 (2002).


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.


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Hitoshi Murakami. Jun Murakami. Miyuki Okamoto. Toshie Takata. Yoshiyuki Yokota. "Kashaev's Conjecture and the Chern-Simons Invariants of Knots and Links." Experiment. Math. 11 (3) 427 - 435, 2002.


Published: 2002
First available in Project Euclid: 9 July 2003

zbMATH: 1117.57300
MathSciNet: MR1959752

Primary: 57M25 , 57M27 , 57M50
Secondary: 17B37 , 41A60 , 81R50

Keywords: Chern-Simons invariant , colored Jones polynomial , Kashaev's conjecture , Volume , Volume conjecture

Rights: Copyright © 2002 A K Peters, Ltd.


Vol.11 • No. 3 • 2002
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