**BİLKENT
ALGEBRAIC **

TOPOLOGY SEMINAR

**"Filtrations of **

**Classifying Spaces"**

By

# CİHAN OKAY

**(University of British
Columbia at Vancouver)**

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**Abstract:
**Let G be a discrete group.
I will construct certain subspaces B(q,G) of the usual
classifying space BG that are obtained from the descending central series of
free groups. When q=2 these spaces capture information about the commutativity in G. I will describe a group theoretic
condition which implies that the space B(2,G) is not
an Eilenberg-Maclane space of type K(\pi,1). This
applies to examples including extraspecial p–groups, symmetric
groups, and general linear groups.

**Date: ****Thursday, June 12, 2014**

**Time: ****14.40-15.30**

**Place: ****Mathematics Seminar Room,
SA-141**

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**All are most cordially invited.**

Tea and cookies will be served after the talk.