Generalised Miller–Morita–Mumford classes for block bundles and topological bundles

Ebert, Johannes; Randal-Williams, Oscar

doi:10.2140/agt.2014.14.1181

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Generalised Miller–Morita–Mumford classes for block bundles and topological bundles

Johannes Ebert and Oscar Randal-Williams

Algebraic & Geometric Topology 14 (2014) 1181–1204

DOI: 10.2140/agt.2014.14.1181

Abstract

The most basic characteristic classes of smooth fibre bundles are the generalised Miller–Morita–Mumford classes, obtained by fibre integrating characteristic classes of the vertical tangent bundle. In this note we show that they may be defined for more general families of manifolds than smooth fibre bundles: smooth block bundles and topological fibre bundles.

Keywords

cohomology of diffeomorphism groups, Miller–Morita–Mumford classes, block diffeomorphisms

Mathematical Subject Classification 2010

Primary: 55R40, 57R20

Secondary: 55R60, 57N55

References

Publication

Received: 28 July 2013

Revised: 1 October 2013

Accepted: 16 October 2013

Published: 21 March 2014

Authors

Johannes Ebert
Mathematisches Institut der Westfälischen Wilhelms-Universität Münster Einsteinstr. 62 48149 Münster Germany

Oscar Randal-Williams
Centre for Mathematical Sciences University of Cambridge Wilberforce Road Cambridge CB3 0WB UK

Volume 14, issue 2 (2014)