Higher torsion and secondary transfer of unipotent bundles

Badzioch, Bernard; Dorabiała, Wojciech

doi:10.2140/gt.2016.20.1807

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Higher torsion and secondary transfer of unipotent bundles

Bernard Badzioch and Wojciech Dorabiała

Geometry & Topology 20 (2016) 1807–1857

DOI: 10.2140/gt.2016.20.1807

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.

Keywords

Reidemeister torsion, higher torsion, unipotent bundle

Mathematical Subject Classification 2010

Primary: 19J10

Secondary: 55R10

References

Publication

Received: 27 December 2012

Revised: 26 April 2015

Accepted: 28 October 2015

Published: 15 September 2016

Proposed: Ralph Cohen

Seconded: John Lott, Steve Ferry

Authors

Bernard Badzioch
Department of Mathematics University at Buffalo SUNY 244 Mathematics Building Buffalo, NY 14260 United States

Wojciech Dorabiała
Department of Mathematics Penn State Altoona 3000 Ivyside Park Altoona, PA 16601 United States

Volume 20, issue 4 (2016)