Rigidity of Coxeter groups

Prassidis, Stratos; Spieler, Barry

doi:10.1090/S0002-9947-00-02574-5

Rigidity of Coxeter groups
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by Stratos Prassidis and Barry Spieler

Trans. Amer. Math. Soc. 352 (2000), 2619-2642

DOI: https://doi.org/10.1090/S0002-9947-00-02574-5

Published electronically: March 7, 2000

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Abstract:

Let $W$ be a Coxeter group acting properly discontinuously and cocompactly on manifolds $N$ and $M\ ({\partial }M = {\emptyset })$ such that the fixed point sets of finite subgroups are contractible. Let $f: (N, {\partial }N) \to (M{\times }D^k, M{\times }S^{k-1})$ 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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