Infinite reduced words and the tits boundary of a Coxeter group

Lam, T. and Thomas, A. (2015) Infinite reduced words and the tits boundary of a Coxeter group. International Mathematics Research Notices, 2015(17), pp. 7690-7733. (doi: 10.1093/imrn/rnu182)

Abstract

Let (W,S) be a finite rank Coxeter system with W infinite. We prove that the limit weak order on the blocks of infinite reduced words of W is encoded by the topology of the Tits boundary ∂TX of the Davis complex X of W. We consider many special cases, including W word hyperbolic and X with isolated flats. We establish that when W is word hyperbolic, the limit weak order is the disjoint union of weak orders of finite Coxeter groups. We also establish, for each boundary point ξ, a natural order-preserving correspondence between infinite reduced words which “point towards” ξ, and elements of the reflection subgroup of W which fixes ξ.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Thomas, Dr Anne
• Authors: Lam, T., and Thomas, A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: International Mathematics Research Notices
• Publisher: Oxford University Press
• ISSN: 1073-7928
• ISSN (Online): 1687-0247
• Copyright Holders: Copyright © 2014 The Authors
• First Published: First published in International Mathematics Research Notices 2015(17):7690-7733
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher