The colored Jones polynomial of the figure-eight knot and a quantum modularity

被引：0

作者：

Murakami, Hitoshi ^{[1
]}

机构：

[1] Tohoku Univ, Grad Sch Informat Sci, Aramaki aza Aoba 6-3-09,Aoba Ku, Sendai 9808579, Japan

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2024年 / 76卷 / 02期

关键词：

Colored Jones polynomial; volume conjecture; figure-eight knot; Chern-Simons invariant; Reidemeister torsion; quantum modularity; VOLUME CONJECTURE; INVARIANTS;

D O I：

10.4153/S0008414X23000172

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the asymptotic behavior of the N-dimensional colored Jones polynomial of the figure-eight knot evaluated at exp((u + 2ppv-1)/N), where u is a small real number and p is a positive integer. We show that it is asymptotically equivalent to the product of the p- dimensional colored Jones polynomial evaluated at exp(4Np(2)/(u + 2ppv-1)) and a term that grows exponentially with growth rate determined by the Chern-Simons invariant. This indicates a quantum modularity of the colored Jones polynomial.

引用

页码：519 / 554

页数：36

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