Higher torsion and secondary transfer of unipotent bundles

TL;DR

This paper introduces a new secondary transfer map for unipotent bundles of smooth manifolds, linking it to higher smooth torsion and providing a natural formula for torsion in bundle compositions.

Contribution

It constructs a secondary transfer map that determines higher smooth torsion, offering a novel perspective and a natural composition formula.

Findings

Defines a secondary transfer map for unipotent bundles

Shows the map determines higher smooth torsion

Provides a formula for torsion of composed bundles

Abstract

Given a unipotent bundle of smooth manifolds we construct its secondary transfer map and show that this map determines the higher smooth torsion of the bundle. This approach to higher torsion provides a new perspective on some of its properties. In particular it yields in a natural way a formula for torsion of a composition of two bundles.