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


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

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


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.


coarse homology; Smith theory

2010 Mathematics Subject Classification

20F65, 55Nxx, 57S17

Published 25 January 2012