The equivariant category of proper \(G\)-spaces.
type: Item
instance of: scholarly article
title: The equivariant category of proper \(G\)-spaces.
zbMATH Open document ID: 1039.55002
published in: Rocky Mountain Journal of Mathematics
publication date: 2003-12-03T00:00:00Z
full work available at URL: CONT31-4.html
review text: Let \(G\) be a topological group and \(X\) a \(G\)-space. There is a far developed equivariant version of Lusternik--Schnirelmann theory for the case of \(G\) being compact, but almost nothing is done for \(G\) non-compact. The authors develop the corresponding theory for an interesting class of \(G\)-spaces without the assumption of compactness, in fact, for \(G\)-spaces with proper actions. Two of the main results (Theorems 4.2 and 4.4) are the following; \(\text{cat}(X/G)=n+1\) if: (a) \(X\) is an acyclic \(n\)-manifold, \(n\geq 3\) and \(G\) is a discrete group acting freely and properly with \(X/G\) compact; (b) \(X\) is a (co)homology \(n\)-sphere and \(G\) is a finite group acting freely on \(X\).
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 57S20
Mathematics Subject Classification ID: 57R91
zbMATH DE Number: 2012005
zbMATH Keywords: proper action
zbMATH Keywords: Lusternik-Schnirelmann theory
zbMATH Keywords: equivariant Lusternik--Schnirelmann category
author: Rafael Ayala
author: Francisco F. Lasheras
author: Antonio Quintero
reviewed by: Yuli Rudyak
MaRDI profile type: Publication
OpenAlex ID: W1999834335
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DOI: 10.1216/RMJM/1021249432
description: scientific article; zbMATH DE number 2012005