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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Rigidity of Coxeter groups
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by Stratos Prassidis and Barry Spieler PDF
Trans. Amer. Math. Soc. 352 (2000), 2619-2642 Request permission

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
  • 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
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 2619-2642
  • MSC (1991): Primary 57S25, 57N70, 20F55, 57S30
  • DOI: https://doi.org/10.1090/S0002-9947-00-02574-5
  • MathSciNet review: 1695035