Reidemeister torsion, the Thurston norm and Harvey's invariants

TL;DR

This paper explores the relationship between Reidemeister torsion and Alexander polynomials to establish improved lower bounds on the Thurston norm, unifying and extending previous bounds with a new, elegant approach.

Contribution

It demonstrates how Reidemeister torsion relates to twisted and higher order Alexander polynomials, providing a unified framework for Thurston norm bounds and extending prior results.

Findings

Reidemeister torsion relates to Alexander polynomials

New lower bounds on Thurston norm are established

Unified and extended bounds from previous work

Abstract

Recently twisted and higher order Alexander polynomials were used by Cochran, Harvey, Friedl--Kim and Turaev to give lower bounds on the Thurston norm. We first show how Reidemeister torsion relates to these Alexander polynomials. We then give lower bounds on the Thurston norm in terms of the Reidemeister torsion which contain and extend all the above lower bounds and give an elegant reformulation of the bounds of Cochran, Harvey and Turaev. The Reidemeister torsion approach also gives a natural approach to proving and extending certain monotonicity results of Cochran and Harvey.