Topology & Geometric Group Theory Seminar

Spring 2008

1:30 - 2:30, Malott 207

Thursday, March 6

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 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 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.