On the Alexander polynomial of links in lens spaces

TL;DR

This paper explores the relationship between the Alexander polynomial of links in lens spaces and the classical Alexander polynomial in the 3-sphere, revealing a normalization that satisfies a skein relation in lens spaces.

Contribution

It establishes a connection between Alexander polynomials in lens spaces and the classical case, introducing a normalization that obeys a skein relation.

Findings

Alexander polynomial in lens spaces relates to classical Alexander polynomial in S^3

A normalization of the Alexander polynomial satisfies a skein relation in lens spaces

Provides a method to compute Alexander polynomials for links in lens spaces

Abstract

We show how the Alexander polynomial of links in lens spaces is related to the classical Alexander polynomial of a link in the 3-sphere, obtained by cutting out the exceptional lens space fibre. It follows from these relationship that a certain normalization of the Alexander polynomial satisfies a skein relation in lens spaces.