Simply connected subsets of buildings
by
Bernhard Mühlherr
Université Libre de Bruxelles
Coauthors: Alice Devillers (Brussels)

Buildings have been introduced by Tits in order to study groups of Lie-type. There are essentially two points of view. One can see buildings as simplicial complexes or as chamber systems. In my talk I will choose the second one. Chamber systems arise naturally as a sort of generalized Cayley graphs and it is therefore not surprising, that they are quite useful for investigating presentations of groups.

In my talk I will present a criterion for the simple connectivity of a subset of a simply connected chamber system which is based on filtrations. I will present two applications to group theory, one of which is turns out to be very useful in the classification of the finite simple groups

Date received: March 28, 2006