Flat structures on surface bundles

Jonathan Bowden

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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.

Original languageEnglish
Pages (from-to)2207-2235
Number of pages29
JournalAlgebraic & Geometric Topology
Volume11
Issue number4
DOIs
Publication statusPublished - Sep 2011
Externally publishedYes

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