On the construction and the topological invariance of the Pontryagin classes

Andrew Ranicki; Michael Weiss

doi:10.1007/s10711-010-9527-2

On the construction and the topological invariance of the Pontryagin classes

Andrew Ranicki, Michael Weiss

Mathematical Science

University of Edinburgh

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We use sheaves and algebraic L-theory to construct the rational Pontryagin classes of fiber bundles with euclidean space fibers. This amounts to an alternative proof of Novikov's theorem on the topological invariance of the rational Pontryagin classes of vector bundles. Transversality arguments and torus tricks are avoided.

Original language	English
Pages (from-to)	309-343
Number of pages	35
Journal	Geometriae Dedicata
Volume	148
Issue number	1
Early online date	18 Aug 2010
DOIs	https://doi.org/10.1007/s10711-010-9527-2
Publication status	Published - Oct 2010

Keywords

L-theory
characteristic classes
sheaves
Poincare duality

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10.1007/s10711-010-9527-2

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AB - We use sheaves and algebraic L-theory to construct the rational Pontryagin classes of fiber bundles with euclidean space fibers. This amounts to an alternative proof of Novikov's theorem on the topological invariance of the rational Pontryagin classes of vector bundles. Transversality arguments and torus tricks are avoided.

KW - L-theory

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KW - sheaves

KW - Poincare duality

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JO - Geometriae Dedicata

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On the construction and the topological invariance of the Pontryagin classes

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Keywords

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