** "Geometry and Analysis on Groups" Research Seminar **

**Time:** 2018.05.15, 15:00–17:00

**Location:** Seminarraum 10, Oskar-Morgenstern-Platz 1, 2.Stock

**Title:** "Classifying space for proper actions for groups
admitting a strict fundamental domain."

**Speaker:** Tomasz
Prytula (University of Southampton)

**Abstract:**
For an infinite discrete group \(G\), the *classifying space for
proper actions* \(\underline{E}G\) is a proper
\(G\)‐CW–complex \(X\), such that for every finite subgroup
\(F\subset G\) the fixed set \(X^F\) is contractible. In a joint work
with Nansen Petrosyan we describe a procedure of constructing new
models for \(\underline{E}G\) out of the standard ones, provided the
action of \(G\) on \(\underline{E}G\) admits a strict fundamental
domain. Our construction is of combinatorial nature, and it depends
only on the structure of the fundamental domain. The resulting model
is often much 'smaller' than the old one, and thus it is well-suited
for (co-)homological computations. Before outlining the construction,
I shall give some background on the space \(\underline{E}G\). I will
also discuss some examples and applications in the context of Coxeter
groups, graph products of finite groups and automorphism groups of
buildings.