Twisted Reidemeister torsion, the Thurston norm and fibered manifolds

TL;DR

This paper establishes that the twisted Reidemeister torsion for fibered classes in 3-manifolds is monic and provides lower bounds on the Thurston norm, correcting previous proofs and offering alternative arguments.

Contribution

It proves the monic property of twisted Reidemeister torsion for fibered classes and demonstrates its use in bounding the Thurston norm, fixing past errors and simplifying proofs.

Findings

Twisted Reidemeister torsion is monic for fibered classes.

Provides lower bounds on the Thurston norm using torsion.

Corrects a flawed proof from previous literature.

Abstract

We prove that the twisted Reidemeister torsion of a 3-manifold corresponding to a fibered class is monic and we show that it gives lower bounds on the Thurston norm. The former fixes a flawed proof in [FV10], the latter gives a quick alternative argument for the main theorem of [FK06].