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arxiv: 1103.3199 · v1 · pith:7OFWDP3Wnew · submitted 2011-03-16 · 🧮 math.GT · math.SG

Flat structures on surface bundles

classification 🧮 math.GT math.SG
keywords bundlessurfaceflatformulaabelianisationbundlecalabicertain
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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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