**BİLKENT
ALGEBRA **

TOPOLOGY SEMINAR

**"Finite Group Actions on Spheres with
Rank One Isotropy"**

By

# ERGÜN YALÇIN

# (Bilkent University)

**Abstract:** In this talk I will present some recent results that we obtained
joint with Ian Hambleton on finite group actions on
spheres. The problem that we are interested in is to classify all finite groups
that can act on a finite CW-complex homotopy equivalent
to a sphere with rank one isotropy. We were able to find some conditions on
rank two finite groups which allow us to construct such actions with rank one
prime power isotropy. The main technical result is a construction method that
gives actions on finite homotopy spheres of a finite
group G when one is provided with a family of representations of Sylow p-subgroups of G which respect fusion in G.

**Date: ****Monday, March 18, 2013**

**Time: ****13.40-14.30**

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

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**All are most cordially invited.**

Tea and cookies will be served after the talk.