Volume 25, issue 7 (2021)

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Rational Pontryagin classes of Euclidean fiber bundles

Michael S Weiss

Geometry & Topology 25 (2021) 3351–3424
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
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