Finiteness properties of groups acting on twin buildings
by
Peter Abramenko
University of Virginia

A natural question concerning the structure of a discrete groups G is whether G is finitely generated, finitely presented, and more generally, of type F_n (or FP_n). These questions are typically analyzed by studying the action of G on suitable (highly connected) spaces, e.g. symmetric spaces or Bruhat-Tits buildings (or products of these) in the case of S-arithmetic groups. It turns out that for some S-arithmetic groups (like SL_n(F_q[t,1/t])) as well as for certain Kac-Moody groups over finite fields, the appropriate space on which G acts is a twin building. I will give a short overview on known finiteness properties of some groups acting on twin buildings and discuss some interesting open problems.

Date received: February 27, 2009