## Topology & Geometric Group Theory Seminar

## Fall 2009

### 1:30 – 2:30, Malott 203

Thursday, October 8

**Will
Dison**, University of Bristol

*Dehn functions of Bestvina–Brady groups*

Bestvina–Brady groups were introduced to solve the long-standing
question of whether the homological and homotopical finiteness
properties F_{n} and FP_{n} are equivalent. The Dehn
function is a group invariant that (in some sense) measures the
complexity of the word problem of a given group. It also has a
geometric interpretation in terms of bounding the areas of filling
discs of loops. In this talk I will give some background and
introduction to these two topics, before outlining a proof of the
following result: Every finitely presented Bestvina–Brady group
has at worst a quartic Dehn function.

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