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}
}
  • J. Hillman
  • Published 2013
  • Mathematics
  • Geometry and Topology Monographs
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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