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 ~K^iso₁(A) to an element of the absolute group K₁^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

Primary: 57Q10

References

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Publication

Received: 2005
Accepted: 2007
Published: 16 March 2007
Proposed: Tom Goodwillie
Seconded: Wolfgang Lueck, Steve Ferry

Authors