Geometry & Topology 11 (2007) 251–314

DOI: 10.2140/gt.2007.11.251

arXiv: math.AT/0502353

Abstract

We express the signature modulo 4 of a closed, oriented, 4k–dimensional PL manifold as a linear combination of its Euler characteristic and the new absolute torsion invariant defined by Korzeniewski [Absolute Whitehead torsion, Geom. Topol. 11 (2007) 215--249]. Let F→E→B be a PL fibre bundle, where F, E and B are closed, connected, and compatibly oriented PL manifolds. We give a formula for the absolute torsion of the total space E in terms of the absolute torsion of the base and fibre, and then combine these two results to prove that the signature of E is congruent modulo 4 to the product of the signatures of F and B.

Keywords

signature, fibre bundle, multiplicative

Mathematical Subject Classification

Primary: 55R25

References

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Publication

Received: 2005
Accepted: 2007
Published: 16 March 2007
Proposed: Tom Goodwillie
Seconded: Colin Rourke, Peter Teichner

Authors