The homology of a space on which a reflection group acts
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.
scientific article; zbMATH DE number 4015733