#### Volume 19 (2015)

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Sections of surface bundles

### Jonathan A Hillman

Geometry & Topology Monographs 19 (2015) 1–19
 arXiv: 1309.3803
##### Abstract

Let $p:E\to B$ be a bundle projection with base $B$ and fibre $F$ aspherical closed connected surfaces. We review what algebraic topology can tell us about such bundles and their total spaces and then consider criteria for $p$ to have a section. In particular, we simplify the cohomological obstruction, and show that the transgression ${d}_{2,0}^{2}$ in the homology LHS spectral sequence of a central extension is evaluation of the extension class. We also give several examples of bundles without sections.

##### Keywords
factor set, extension, lantern relation, section, surface bundle, transgression
##### Mathematical Subject Classification 2010
Primary: 20K35
Secondary: 55R10, 57N13