Homology, Homotopy and Applications

Volume 13 (2011)

Number 2

Coarse geometry and P. A. Smith theory

Pages: 73 – 102

DOI: https://dx.doi.org/10.4310/HHA.2011.v13.n2.a6

Authors

Ian Hambleton (Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada)

Lucian Savin (Bank of Montreal, Toronto, Ontario, Canada)

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 finite p-group actions on metric spaces of finite asymptotic dimension, which relates the coarse homology of the bounded fixed set to the coarse homology of the total space.

Keywords

coarse homology, Smith theory

2010 Mathematics Subject Classification

20F65, 55Nxx, 57S17

Published 25 January 2012