Coarse Geometry and P. A. Smith Theory

Abstract

We define a generalization of the fixed point set, called the bounded fixed set, for a group acting by isometries on a metric space. An analogue of the P. A. Smith theorem is proved for metric spaces of finite asymptotic dimension, which relates the coarse homology of the bounded fixed set to the coarse homology of the total space.Comment: In this version: improvements to the exposition and Theorem B added (29 pages