Absolute Whitehead torsion

Korzeniewski, Andrew

doi:10.2140/gt.2007.11.215

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Absolute Whitehead torsion

Andrew Korzeniewski

Geometry & Topology 11 (2007) 215–249

DOI: 10.2140/gt.2007.11.215

arXiv: math/0502349

Abstract

We refine the Whitehead torsion of a chain equivalence of finite chain complexes in an additive category $A$ from an element of ${\tilde{K}}_{1}^{iso} (A)$ to an element of the absolute group $K_{1}^{iso} (A)$ . We apply this invariant to symmetric Poincaré complexes and identify it in terms of more traditional invariants. In the companion paper (joint with Ian Hambleton and Andrew Ranicki) this new invariant is applied to obtain the multiplicativity of the signature of fibre bundles mod 4.

Keywords

Whitehead torsion

Mathematical Subject Classification 2000

Primary: 57Q10

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Publication

Published: 16 March 2007

Proposed: Tom Goodwillie

Seconded: Wolfgang Lueck and Steve Ferry

Authors

Andrew Korzeniewski
School of Mathematics University of Edinburgh Edinburgh EH9 3JZ United Kingdom

Volume 11, issue 1 (2007)