The Thurston norm and twisted Alexander polynomials

TL;DR

This paper demonstrates that twisted Alexander polynomials can effectively detect the Thurston norm in irreducible 3-manifolds, expanding understanding of their topological properties.

Contribution

It proves that twisted Alexander polynomials detect the Thurston norm for all irreducible 3-manifolds except closed graph manifolds, utilizing recent advances in 3-manifold theory.

Findings

Twisted Alexander polynomials detect the Thurston norm in irreducible 3-manifolds.

The result applies to all irreducible 3-manifolds except closed graph manifolds.

The proof leverages recent breakthroughs by Agol, Przytycki-Wise, and Wise.

Abstract

Using recent results of Agol, Przytycki-Wise and Wise we show that twisted Alexander polynomials detect the Thurston norm of any irreducible 3-manifold which is not a closed graph manifold.