Damian Osajda (Universitat Wien)
Fixed point theorem for systolic complexes
(Joint with Victor Chepoi from Marseille) We prove that any finite group acting on a
(weakly) systolic (i.e. simplicially non-positively curved) complex fixes a point.
This is a systolic counterpart of a similar CAT(0) result. As consequences we show the
following results. A (weakly) systolic group contains only finitely many conjugacy
classes of finite subgroups. A free product of systolic groups amalgamated over a finite
group is systolic. (Weakly) Systolic complexes are classifying spaces for finite
subgroups of (weakly) systolic groups.