Rational Pontryagin classes of Euclidean fiber bundles

Weiss, Michael S

doi:10.2140/gt.2021.25.3351

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Rational Pontryagin classes of Euclidean fiber bundles

Michael S Weiss

Geometry & Topology 25 (2021) 3351–3424

DOI: 10.2140/gt.2021.25.3351

Abstract

The Pontryagin classes of an $m$ –dimensional real vector bundle satisfy well-known vanishing relations due to their close relationship with the Chern classes of the complexified vector bundle. It is also known that the rational Pontryagin classes qualify as characteristic classes for Euclidean fiber bundles, ie bundles whose fibers are homeomorphic to $m$ –dimensional Euclidean space. In this more general setting of fiber bundles, the vanishing relations which one has for vector bundles fail to hold.

Keywords

Pontryagin classes, homeomorphisms, diffeomorphisms

Mathematical Subject Classification 2010

Primary: 57N55, 57R20

Secondary: 57R40

References

Publication

Received: 19 December 2018

Revised: 9 October 2020

Accepted: 5 December 2020

Published: 25 January 2022

Proposed: Jesper Grodal

Seconded: Paul Seidel, Haynes R Miller

Authors

Michael S Weiss
Faculty of Mathematics and Computer Science University of Muenster Muenster Germany

Volume 25, issue 7 (2021)