Infinite reduced words and the Tits boundary of a Coxeter group

2013/01/05 by Lam, Thomas, Thomas, Anne · 2 citations
#20F55 #20F65 #52C35 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1301.0873

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 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.

Cited by

• Boundary actions of CAT(0) spaces: topological freeness and applications to C^*-algebras
• Universal C^∗-Algebras from Graph Products: Structure and Applications

Related

• Reduced expression of minimal infinite reduced words of affine Weyl groups
• On boundaries of parabolic subgroups of Coxeter groups
• On boundaries of Coxeter groups and topological fractal structures
• Coarse decompositions of boundaries for CAT(0) groups
• A series of word-hyperbolic Coxeter groups