Sections of surface bundles
Abstract
A bundle with base B and fibre F aspherical closed surfaces has a section if and only if the action :π1(B)Out(π1(F)) factors through Aut(π1(F)) and a cohomology class is 0. We simplify and make more explicit the latter condition. We also show that the transgression d22,0 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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