Twisted Reidemeister torsion and the Thurston norm: graph manifolds and finite representations

TL;DR

This paper demonstrates that the Thurston norm of irreducible 3-manifolds, including graph manifolds, can be detected using twisted Reidemeister torsions from integral and finite field representations, extending previous results.

Contribution

It extends the detection of the Thurston norm via twisted Reidemeister torsions to all graph manifolds, which were not covered in earlier work.

Findings

Thurston norm can be detected using twisted Reidemeister torsions.

Results apply to all graph manifolds.

Detection works over both integral and finite field representations.

Abstract

We show that the Thurston norm of any irreducible 3-manifold can be detected using twisted Reidemeister torsions corresponding to integral representations and also corresponding to representations over finite fields. In particular our result holds for all graph manifolds, these are not covered by the earlier work of the first author and Vidussi.