New York Journal of Mathematics
Volume 10 (2004) 151-167


Gábor Moussong and Stratos Prassidis

Equivariant rigidity theorems

Published: April 28, 2004
Keywords: Coxeter groups, reflection groups, topological rigidity
Subject: Primary 57S30; Secondary 20F55, 57N99, 57S25

Let Γ be a discrete group which is a split extension of a group Δ by a Coxeter group W, with Δ acting on W by Coxeter graph automorphisms with kernel Δ0. Let Mi, i = 1,2, be two Γ-manifolds (possibly with boundary) such that the isotropy groups are finite and the fixed point sets are contractible and W acts by reflections. Let f be a Γ-homotopy equivalence between them that it is a homeomorphism outside the orbit of a compact subset. Then f is Γ-homotopic to a Γ-homeomorphism, provided that certain finite extensions of Δ0 that fix the faces of the fundamental domains are topologically rigid groups.


The first author was partially supported by Hungarian Nat. Found. for Sci. Research Grant T032478.

Author information

Gábor Moussong:
Department of Geometry, Eötvös Loránd University, P. O. Box 120 Budapest, Hungary H-1518

Stratos Prassidis:
Department of Mathematics {&} Statistics, Canisius College, Buffalo, NY 14208