Sections of surface bundles
Geometric Topology
2018-07-10 v4 Group Theory
Abstract
A bundle with base and fibre aspherical closed surfaces has a section if and only if the action factors through and a cohomology class is 0. We simplify and make more explicit the latter condition. We also show that the transgression 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.
Keywords
Cite
@article{arxiv.1309.3803,
title = {Sections of surface bundles},
author = {Jonathan A. Hillman},
journal= {arXiv preprint arXiv:1309.3803},
year = {2018}
}
Comments
Some new background material. Section on flat fibred case rewritten. In v3, details of Endo's example corrected and commentary added to final section on questions