Equivariant rigidity theorems
type: Item
instance of: scholarly article
title: Equivariant rigidity theorems
zbMATH Open document ID: 1073.57018
author: Gábor Moussong
author: Stratos Prassidis
published in: The New York Journal of Mathematics
publication date: 2005-05-09T00:00:00Z
full work available at URL: https://eudml.org/doc/125203
full work available at URL: 10-9nf.htm
review text: Let \(\Gamma\) be a discrete group which is a split extension of a group \(\Delta\) by a Coxeter group \(W\), with \(\Delta\) acting on \(W\) by Coxeter graph automorphisms with kernel \(\Delta_{0}\). Let \(M_{1},M_{2}\) be two \(\Gamma\)-manifolds such that the isotropy groups are finite, the fixed point sets are contractible and \(W\) acts by reflections; let further \(f:M_{1} \rightarrow M_{2}\) be a \(\Gamma\)-homotopy equivalence that is a homeomorphism outside the orbit of a compact subset. The main result asserts that if certain finite extensions of \(\Delta_{0}\) that fix the faces of the fundamental domains are topologically rigid groups then \(f\) is \(\Gamma\)-homotopic to a \(\Gamma\)-homeomorphism.
reviewed by: Gheorghe Pitiş
Mathematics Subject Classification ID: 57S30
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 57N99
Mathematics Subject Classification ID: 57S25
zbMATH DE Number: 2166319
zbMATH Keywords: Coxeter group
zbMATH Keywords: reflection group
zbMATH Keywords: topological rigidity
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2166319