# Sections of surface bundles

@article{Hillman2013SectionsOS, title={Sections of surface bundles}, author={Jonathan A. Hillman}, journal={Geometry and Topology Monographs}, year={2013}, volume={19}, pages={1-19} }

A bundle with base $B$ and fibre $F$ aspherical closed surfaces has a section if and only if the action $:\pi_1(B)\to{Out}(\pi_1(F))$ factors through $Aut(\pi_1(F))$ and a cohomology class is 0. We simplify and make more explicit the latter condition. We also show that the transgression $d^2_{2,0}$ in the homology LHS spectral sequence of a central extension is evaluation of the extension class. Examples with hyperbolic fibre and no section (based on ideas of Endo) added.

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