The<i>L</i>²-Alexander torsion of 3-manifolds

Abstract

We introduce L 2 -Alexander torsions for 3-manifolds, which can be viewed as a generalization of the L 2 -Alexander invariant of Li–Zhang. We state the L 2 -Alexander torsions for graph manifolds and we partially compute them for fibered manifolds. We furthermore show that, given any irreducible 3-manifold there exists a coefficient system such that the corresponding L 2 -torsion detects the Thurston norm.