Volume 11, issue 4 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Flat structures on surface bundles

Jonathan Bowden

Algebraic & Geometric Topology 11 (2011) 2207–2235
Abstract

We show that there exist flat surface bundles with closed leaves having nontrivial normal bundles. This leads us to compute the abelianisation of surface diffeomorphism groups with marked points. We also extend a formula of Tsuboi that expresses the Euler class of a flat circle bundle in terms of the Calabi invariant of certain Hamiltonian diffeomorphisms to surfaces of higher genus and derive a similar formula for the first MMM–class of surface bundles with punctured fibre.

Keywords
diffeomorphism group, mapping class group, foliation, symplectic topology, group cohomology, characteristic class of surface bundle
Mathematical Subject Classification 2010
Primary: 37E30, 57R30, 57R50
Secondary: 57R17
References
Publication
Received: 3 May 2011
Revised: 7 July 2011
Accepted: 8 July 2011
Published: 9 August 2011
Authors
Jonathan Bowden
Institut für Mathematik
Universität Augsburg
Universitätsstr 14
D-86159 Augsburg
Germany
http://www.math.uni-augsburg.de/de/prof/diff/arbeitsgruppe/bowden