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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Rigidity of Coxeter groups


Authors: Stratos Prassidis and Barry Spieler
Journal: Trans. Amer. Math. Soc. 352 (2000), 2619-2642
MSC (1991): Primary 57S25, 57N70, 20F55, 57S30
Published electronically: March 7, 2000
MathSciNet review: 1695035
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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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Additional Information

Stratos Prassidis
Affiliation: Coordenação de Pós-Graduação em Matemática, Rua Mário Santos Braga, Valonguinho Niterói, RJ 24020-005, Brazil

Barry Spieler
Affiliation: Division of Science and Mathematics, Birmingham-Southern College, Birmingham, Alabama 35254

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02574-5
PII: S 0002-9947(00)02574-5
Keywords: Coxeter groups, reflection groups, rigidity theorems, equivariant topological Whitehead group
Received by editor(s): November 14, 1997
Published electronically: March 7, 2000
Additional Notes: The first author was supported in part by Vanderbilt University Summer Research Fellowship, and by National Science Foundation Grant DMS-9504479
Article copyright: © Copyright 2000 American Mathematical Society