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.

AMS Subject Classification: Primary 20J05; secondary 57N13.