Mathematical Conversations

Which spaces can be the fixed point sets of actions of $G$ on finite cell-complexes of a given homotopy type? The general answers to such questions, for $G$ not a group of prime-power order, will be expressed, even for non-simply-connected spaces, just in terms of conditions on Euler characteristics, These new results generalize classical work of R. Oliver. Time allowing, we will also contrast these results, including for non-simply connected spaces, to quite different kinds of results for some restricted kinds of actions, e.g., for semi-free actions. All these results are joint with Shmuel Weinberger (University of Chicago) and Min Yan (Hong Kong University of Science and Technology)