The homology of a space on which a reflection group acts
type: Item
instance of: scholarly article
title: The homology of a space on which a reflection group acts
zbMATH Open document ID: 0625.57020
DOI: 10.1215/S0012-7094-87-05506-2
author: Michael W. Davis
published in: Duke Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: Let (W,S) be a Coxeter system, X a CW-complex and \(\{X_ s\}^ a \)family of subcomplexes indexed by S. There is a standard way to form a CW-complex A containing X on which W acts so that \(A=WX\) and the \(X_ s\) play a role analogous to the mirrors in a kaleidoscope. The author computes the homology \(H_*(A)\) as a direct sum of relative homology groups \(H_*(X,Y_ w)\) where \(w\in W\) and \(Y_ w\subset X\) is a certain subcomplex for each w. When W is finite, the \({\mathbb{Q}}W\)-module structure on \(H_*(A, {\mathbb{Q}})\) is also determined.
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 55N99
Mathematics Subject Classification ID: 51F15
Mathematics Subject Classification ID: 20F38
zbMATH DE Number: 4015733
zbMATH Keywords: reflection group
zbMATH Keywords: actions of Coxeter groups on CW-groups
zbMATH Keywords: homology groups of certain spaces
zbMATH Keywords: Coxeter system
MaRDI profile type: Publication
cites work: Q5580319
cites work: Groups generated by reflections and aspherical manifolds not covered by Euclidean space
cites work: A decomposition of the group algebra of a finite Coxeter group
full work available at URL: s0012-7094-87-05506-2
OpenAlex ID: W2073810662
description: scientific article; zbMATH DE number 4015733