Equivariant rigidity theorems
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.
scientific article; zbMATH DE number 2166319