## Topology & Geometric Group Theory Seminar

## Spring 2008

### 1:30 - 2:30, Malott 207

Thursday, March 6

**Peter
Abramenko**, University of Virginia

*Finiteness properties of some discrete groups*

There are various finiteness conditions for infinite groups. Maybe
the two most important ones are that a group G is finitely generated
or finitely presented. These two finiteness conditions can be
interpreted topologically and lead to the more general concept of
groups of type F_{m}, with G being of type F_{1} iff
it is finitely generated and of type F_{2} iff it is finitely
presented.

In this talk, I will survey some results about the
F_{m}-properties of certain discrete subgroups of locally
compact groups like SL_{n}(Z) (discrete in SL_{n}(R))
or SL_{n}(F_{q}[t]) (discrete in
SL_{n}(F_{q}((1/t))), more generally: of certain
S-arithmetic groups. Some of these groups (in the function field
case) are closely related to Kac-Moody groups over finite fields, and
I shall report on some results concerning the F_{m}-properties
of these groups as well.

In most of the cases mentioned above, an important ingredient of the
proofs is a careful study of the action of these groups on the
corresponding (twin) buildings.

Back to seminar home page.