## Sections of surface bundles

### Jonathan A. Hillman

#### Abstract

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.

Keywords: factor set; section; surface bundle.

: Primary 20J05; secondary 57N13.

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 Monday, September 9, 2013