Knot invariants from representations of braids by automorphisms of a free group

TL;DR

This paper introduces a novel method for computing Alexander polynomials of knots and links using automorphisms of free groups derived from braid representations, and compares these with other braid group invariants.

Contribution

It presents an alternative computational approach for Alexander polynomials and explores new braid group invariants from Wada's representations.

Findings

New computational method for Alexander polynomials

Comparison of isotopic invariants from different braid representations

Insights into relationships between various braid group invariants

Abstract

We describe an alternative way of computing Alexander polynomials of knots/links, based on the Artin representation of the corresponding braids by automorphisms of a free group. Then we apply the same method to other representations of braid groups discovered by Wada and compare the corresponding isotopic invariants to Alexander polynomials.