Flat structures on surface bundles

Details Flat structures on surface bundles Flat structures on surface bundles

2011-03-16

arxiv.org/abs/1103.3199v1

Algebr. Geom. Topol. 11 (2011), no. 4, 2207--2235

Mathematics

Geometric Topology

Scientific paper

We show that there exist flat surface bundles with closed leaves having non-trivial 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.

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