**SMS scnews item created by Stephan Tillmann at Thu 9 Oct 2014 1016**

Type: Seminar

Distribution: World

Expiry: 8 Jan 2015

**Calendar1: 15 Oct 2014 1100-1200**

**CalLoc1: Carslaw 535A**

Auth: tillmann@p710.pc (assumed)

### Geometry-Topology-Analysis Seminar

# Sections of Surface Bundles

### Jonathan Hillman (Sydney)

GTA Seminar - Wednesday, 15 October, 11:00-12:00 in Carlaw 535A

##
Sections of Surface Bundles

An \(F\)-bundle \(p:E\to{B}\) is a continuous map with fibres
\(p^{-1}(b)\) homeomorphic to \(F\), for all \(b\in{B}\),
and which is locally trivial:
the base \(B\) has a covering by open sets \(U\) over each of which \(p\)
is equivalent to the obvious projection of \(U\times{F}\) onto \(U\).
(Thus \(p\) is a family of copies of \(F\), parametrized by \(B\).)

We shall assume that \(B\) and \(F\) are closed aspherical surfaces.
Such bundles are then determined by the associated
fundamental group extensions
\[
1\to\pi_1(F)\to\pi_1(E)\to\pi_1(B)\to1.
\]
We review this connection,
and consider when such a bundle \(p\) has a section,
i.e., a map \(s:B\to {E}\) such that \(ps=id_B\).
If time permits we may say something about recent work by Nick Salter
on the extent to which \(\pi_1(E)\) alone determines the bundle.

Please join us for lunch after the talk!