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 Fm, with G being of type F1 iff it is finitely generated and of type F2 iff it is finitely presented.

In this talk, I will survey some results about the Fm-properties of certain discrete subgroups of locally compact groups like SLn(Z) (discrete in SLn(R)) or SLn(Fq[t]) (discrete in SLn(Fq((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 Fm-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.

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