Difference equation of the colored Jones polynomial for torus knot

被引：44

作者：

Hikami, K ^{[1
]}

机构：

[1] Univ Tokyo, Dept Phys, Grad Sch Sci, Bunkyo Ku, Tokyo 1130033, Japan

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2004年 / 15卷 / 09期

关键词：

torus knot; Jones polynomial; A-polynomial; Alexander polynomial; q-hypergeometric function;

D O I：

10.1142/S0129167X04002582

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the N-colored Jones polynomial for the torus knot T-s,T-t satisfies the second order difference equation, which reduces to the first order difference equation for a case of T-2,T-2m+1. We show that the A-polynomial of the torus knot can be derived from the difference equation. Also constructed is a q-hypergeometric type expression of the colored Jones polynomial for T-2,T-2m+1.

引用

页码：959 / 965

页数：7

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