Homology, Homotopy and Applications

Coarse geometry and P. A. Smith theory

Ian Hambleton and Lucian Savin

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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.

Article information

Source
Homology Homotopy Appl., Volume 13, Number 2 (2011), 73-102.

Dates
First available in Project Euclid: 30 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.hha/1335806743

Mathematical Reviews number (MathSciNet)
MR2846159

Zentralblatt MATH identifier
1232.57025

Subjects
Primary: 57S17: Finite transformation groups 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 55N

Keywords
Coarse homology Smith theory

Citation

Hambleton, Ian; Savin, Lucian. Coarse geometry and P. A. Smith theory. Homology Homotopy Appl. 13 (2011), no. 2, 73--102. https://projecteuclid.org/euclid.hha/1335806743


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