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arXiv · 1309.3803

Sections of surface bundles

Jonathan A. Hillman
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Abstract

A bundle with base $B$ and fibre $F$ aspherical closed surfaces has a section if and only if the action $:π_1(B)\to{Out}(π_1(F))$ factors through $Aut(π_1(F))$ 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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Jonathan A. Hillman. 2014-09-19. Sections of surface bundles. https://doi.org/10.2140/gtm.2015.19.1

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