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The
signature of a fibre bundle is multiplicative mod 4
Ian Hambleton, Andrew Korzeniewski and Andrew Ranicki |
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Geometry & Topology 11 (2007) 251–314
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arXiv: math.AT/0502353 |
Abstract |
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We express the signature modulo 4 of a closed, oriented, –dimensional 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 be a fibre bundle, where , and are closed, connected, and compatibly oriented manifolds. We give a formula for the absolute torsion of the total space in terms of the absolute torsion of the base and fibre, and then combine these two results to prove that the signature of is congruent modulo 4 to the product of the signatures of and . |
Keywords
signature, fibre bundle, multiplicative
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Mathematical Subject Classification 2000
Primary: 55R25
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References |
Forward citations |
Publication
Published: 16 March 2007
Proposed: Tom Goodwillie
Seconded: Colin Rourke and Peter Teichner
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Authors |
| Ian Hambleton | |
| Department of Mathematics &
Statistics McMaster University Hamilton Ontario L8S 4K1 Canada |
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| Andrew Korzeniewski | |
| School of Mathematics University of Edinburgh Edinburgh EH9 3JZ United Kingdom |
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| Andrew Ranicki | |
| School of Mathematics University of Edinburgh Edinburgh EH9 3JZ United Kingdom |
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