The L^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 polynomial 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.

47 pages v3: fixed many typos, updated references and improved the exposition, following the referees suggestions

References in corpus (2)

• Mixed 3-manifolds are virtually special
• $L^2$-Alexander invariant for knots

Cited by in corpus (4)

• Twisting $L^2$-invariants with finite-dimensional representations
• Degree of $L^2$-Alexander torsion for 3-manifolds
• Survey on approximating L^2-invariants by their classical counterparts: Betti numbers, torsion invariants and homological growth
• The $L^2$-Alexander torsion for Seifert fiber spaces