Rigidity of Coxeter groups

Let W be a Coxeter group acting properly discontinuously and cocompactly on manifolds N and M (9M = 0) such that the fixed point sets of finite subgroups are contractible. Let f : (N, &N) -* (Mx Dk, M XSk1) be a W-homotopy equivalence which restricts to a W-homeomorphism on the boundary. Under an assumption on the three dimensional fixed point sets, we show that then f is W-homotopic to a W-homeomorphism.

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