RIGIDITY THEOREMS FOR RIGHT ANGLED REFLECTION GROUPS

Let T be a right angled reflection group. Let M and M' be Coxeter manifolds. Then any T-map f:M—fM' is T-homotopic to a homeo- morphism Introduction. This paper contains the results given in the author's Ph.D. the- sis. Davis in (9), showed that in every dimension > 4, there exists a cocompact reflection group on a contractible manifold not homeomorphic to an Euclidean space. Also he gave the first example of a closed aspherical manifold not covered by Euclidean space. Davis construction provides an infinite Coxeter group acting locally smoothly, effectively and properly discontinuously on a contractible manifold with compact quotient.

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