The head and tail conjecture for alternating knots

TL;DR

This paper studies the stabilization of the extremal coefficients of the colored Jones polynomial for alternating and adequate links using skein theory techniques.

Contribution

It proves the stabilization of head and tail coefficients for these classes of links, advancing understanding of their polynomial invariants.

Findings

Coefficients stabilize for alternating links.

Coefficients stabilize for adequate links.

Uses skein theory techniques.

Abstract

We investigate the coefficients of the highest and lowest terms (also called the head and the tail) of the colored Jones polynomial and show that they stabilize for alternating links and for adequate links. To do this we apply techniques from skein theory.