Groups with fixed point properties
Friday November 9, 2007
10:30AM - 11:30AM
Speakers:
Tadeusz Januszkiewicz
Abstract:
I will describe a general procedure for construction infinite,
finitely generated (but not finitely presented) groups
with various fixed point properties.
The example I will to concentrate on is a group G as above
which has a fixed point, whenever it acts on
a finite dimensional, contractible ANR.
The construction is done in two steps.
First, a sequence of groups G_n is constructed; whenver G_n acts on a
contractible ANR of dimension less than n, it has a fixed point.
Second, if groups G_n "have enough hyperboilicty", then there exists a common
infinite quotient of them all.
The groups G_n are fundamental groups of simplices of finite groups.
We can arrange them to be hyperbolic.
The existence of fixed point comes Smith theory (in case when all finite
groups on the simplex are p-groups) and homological version of
Helly's theorem.
Tadeusz Januszkiewicz
(Joint work with Goulnara Arzhantseva, Martin Bridson, Ian Leary, Ashot Minasyan and Jacek Swiatkowski)
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