The colored Kauffman skein relation and the head and tail of the colored Jones polynomial

2014/01/18 by Hajij, Mustafa
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1401.4537

Abstract

Using the colored Kauffman skein relation, we study the highest and lowest 4n coefficients of the n^th unreduced colored Jones polynomial of alternating links. This gives a natural extension of a result by Kauffman in regard with the Jones polynomial of alternating links and its highest and lowest coefficients. We also use our techniques to give a new and natural proof for the existence of the tail of the colored Jones polynomial for alternating links.

Related

• The Colored Jones Polynomial and the A-Polynomial of Knots
• An invariant of colored links via skein relation
• On the head and the tail of the colored Jones polynomial
• Stability properties of the colored Jones polynomial
• Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial