TY - JOUR
T1 - Kashaev's conjecture and the chern-simons invariants of knots and links
AU - Murakami, Hitoshi
AU - Murakami, Jun
AU - Okamoto, Miyuki
AU - Takata, Toshie
AU - Yokota, Yoshiyuki
PY - 2002
Y1 - 2002
N2 - R. M. Kashaev conjectured that the asymptotic behavior of the link invariant he introduced [Kashaev 95], 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.
AB - R. M. Kashaev conjectured that the asymptotic behavior of the link invariant he introduced [Kashaev 95], 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.
KW - Chern-simons invariant
KW - Colored jones polynomial
KW - Kashaev’s conjecture
KW - Volume
KW - Volume conjecture
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U2 - 10.1080/10586458.2002.10504485
DO - 10.1080/10586458.2002.10504485
M3 - Article
AN - SCOPUS:0036943077
SN - 1058-6458
VL - 11
SP - 427
EP - 435
JO - Experimental Mathematics
JF - Experimental Mathematics
IS - 3
ER -