Flat structures on surface bundles
Geometric Topology
2014-10-01 v1 Symplectic Geometry
Abstract
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.
Cite
@article{arxiv.1103.3199,
title = {Flat structures on surface bundles},
author = {Jonathan Bowden},
journal= {arXiv preprint arXiv:1103.3199},
year = {2014}
}