The $L^2$-Alexander torsion for Seifert fiber spaces

TL;DR

This paper computes the $L^2$-Alexander torsion for Seifert fiber spaces and graph manifolds, linking it to the Thurston norm, thus advancing understanding of 3-manifold invariants.

Contribution

It introduces explicit calculations of the $L^2$-Alexander torsion for specific 3-manifolds in relation to the Thurston norm, a novel connection in the field.

Findings

Explicit formulas for $L^2$-Alexander torsion in Seifert fiber spaces

Relation established between torsion and Thurston norm

Enhanced understanding of 3-manifold invariants

Abstract

We calculate the $L^2$-Alexander torsion for Seifert fiber spaces and graph manifolds in terms of the Thurston norm.