Volume 14, issue 4 (2010)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Twist-rigid Coxeter groups

Pierre-Emmanuel Caprace and Piotr Przytycki

Geometry & Topology 14 (2010) 2243–2275
Abstract

We prove that two angle-compatible Coxeter generating sets of a given finitely generated Coxeter group are conjugate provided one of them does not admit any elementary twist. This confirms a basic case of a general conjecture which describes a potential solution to the isomorphism problem for Coxeter groups.

Keywords
Coxeter groups, isomorphism problem, twists, rigidity, hierarchy
Mathematical Subject Classification 2000
Primary: 20F10, 20F55
References
Publication
Received: 14 November 2009
Accepted: 13 August 2010
Published: 29 October 2010
Proposed: Benson Farb
Seconded: Joan Birman, Walter Neumann
Authors
Pierre-Emmanuel Caprace
Département de Mathématiques
Université catholique de Louvain
Chemin du Cyclotron 2
1348 Louvain-la-Neuve
Belgium
Piotr Przytycki
Institute of Mathematics
Polish Academy of Sciences
Śniadeckich 8
00-956 Warsaw
Poland
http://www.mimuw.edu.pl/~pprzytyc/