Twist-rigid Coxeter groups

Caprace, Pierre-Emmanuel; Przytycki, Piotr

doi:10.2140/gt.2010.14.2243

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Twist-rigid Coxeter groups

Pierre-Emmanuel Caprace and Piotr Przytycki

Geometry & Topology 14 (2010) 2243–2275

DOI: 10.2140/gt.2010.14.2243

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/

Volume 14, issue 4 (2010)