Equivalence of higher torsion invariants

TL;DR

This paper proves that the smooth torsion invariants for manifold bundles by Dwyer, Weiss, and Williams align with Igusa's higher torsion axioms, establishing their proportionality.

Contribution

It demonstrates the equivalence of the Dwyer-Weiss-Williams smooth torsion with Igusa's higher torsion, confirming their proportional relationship.

Findings

Smooth torsion satisfies Igusa's axioms

Proportionality between Dwyer-Weiss-Williams and Igusa's higher torsion

Unification of different higher torsion invariants

Abstract

We show that the smooth torsion of bundles of manifolds constructed by Dwyer, Weiss, and Williams satisfies the axioms for higher torsion developed by Igusa. As a consequence we obtain that the smooth Dwyer-Weiss-Williams torsion is proportional to the higher torsion of Igusa and Klein.