Flat structures on surface bundles

Bowden, Jonathan

doi:10.2140/agt.2011.11.2207

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Flat structures on surface bundles

Jonathan Bowden

Algebraic & Geometric Topology 11 (2011) 2207–2235

DOI: 10.2140/agt.2011.11.2207

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

Volume 11, issue 4 (2011)