A Note on Alexander Polynomials of 2-Bridge Links

2019/07/08 by Hoste, Jim · 1 citation
#57 M 25 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1907.03812

Abstract

A formula for the Alexander polynomial of a 2-bridge knot or link given by Hartley and also by Minkus has a beautiful interpretation as a walk on the integers. We extend this to the 2-variable Alexander polynomial of a 2-bridge link, obtaining a formula that corresponds to a walk on the 2-dimensional integer lattice.

Cited by

• On the classification of 2-plat 2-knots

Related

• Conway polynomials of two-bridge links
• On Alexander-Conway polynomials of two-bridge links
• Twisted Alexander polynomials of 2-bridge knots
• Local-move-identities for the Z[t,t^-1]-Alexander polynomials of 2-links, the alinking number, and high dimensional analogues
• On zeros of the Alexander polynomial of an alternating knot