# COLLOQUIUM

## Z-Structures on Product Groups

### Carrie Tirel, Ph. D. Defense

UW–Milwaukee

**Monday, August 2, 2010, 1:00 pm, EMS E408**

A *Z**-structure* on a group G, defined by M. Bestvina, is a pair (∧X, Z) of spaces such that ∧X is a compact ER, Z is a *Z*-set in ∧X, G acts properly and cocompactly on X=∧X\Z, and the collection of translates of any compact set in X forms a null sequence in ∧X. It is natural to ask whether a given group admits a *Z*-structure. In this paper, we will show that if two groups each admit a *Z*-structure, then so do their free and direct products.

**Refreshments will be provided in EMS E408 at 12:30.**

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