Volume 11, issue 1 (2007)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The signature of a fibre bundle is multiplicative mod 4

Ian Hambleton, Andrew Korzeniewski and Andrew Ranicki

Geometry & Topology 11 (2007) 251–314

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 2000
Primary: 55R25
References
Forward citations
Publication
Published: 16 March 2007
Proposed: Tom Goodwillie
Seconded: Colin Rourke and Peter Teichner
Authors
Ian Hambleton
Department of Mathematics & Statistics
McMaster University
Hamilton
Ontario
L8S 4K1
Canada
Andrew Korzeniewski
School of Mathematics
University of Edinburgh
Edinburgh
EH9 3JZ
United Kingdom
Andrew Ranicki
School of Mathematics
University of Edinburgh
Edinburgh
EH9 3JZ
United Kingdom