Minimality of the boundary of a right-angled Coxeter system

2006/06/01 by Hosaka, Tetsuya
#20F55 #20F65 #57M07 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0606020

Abstract

In this paper, we show that the boundary ∂Σ(W,S) of a right-angled Coxeter system (W,S) is minimal if and only if W_S is irreducible, where W_S is the minimum parabolic subgroup of finite index in W. We also provide several applications and remarks. In particular, we obtain that for a right-angled Coxeter system (W,S), the set \w^∞ | w∈ W, o(w)=∞\ is dense in the boundary ∂Σ(W,S).

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