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
Author Index
To Appear
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


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.

signature, fibre bundle, multiplicative
Mathematical Subject Classification 2000
Primary: 55R25
Forward citations
Published: 16 March 2007
Proposed: Tom Goodwillie
Seconded: Colin Rourke and Peter Teichner
Ian Hambleton
Department of Mathematics & Statistics
McMaster University
L8S 4K1
Andrew Korzeniewski
School of Mathematics
University of Edinburgh
United Kingdom
Andrew Ranicki
School of Mathematics
University of Edinburgh
United Kingdom