Volume 14, issue 2 (2014)

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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
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