OREGON STATE UNIVERSITY
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Max Forester and Colin Rourke have recently proved a fixed point theorem for finite groups acting on cell complexes of finite (homological) dimension. Their result provides a new proof of a theorem of Jean-Pierre Serre in cohomology of groups that has been influential in classfying finite subgroups of groups given by generators and relators. I will sketch the Forester-Rourke proof and indicate some related ideas and applications.