Addendum to “Dense subsets of the boundary of a Coxeter system”

Hosaka, Tetsuya

doi:10.1090/S0002-9939-05-08307-3

Addendum to “Dense subsets of the boundary of a Coxeter system”
HTML articles powered by AMS MathViewer

by Tetsuya Hosaka PDF

Proc. Amer. Math. Soc. 133 (2005), 3745-3747 Request permission

Abstract:

In this paper, we investigate boundaries of parabolic subgroups of Coxeter groups. Let $(W,S)$ be a Coxeter system and let $T$ be a subset of $S$ such that the parabolic subgroup $W_T$ is infinite. Then we show that if a certain set is quasi-dense in $W$, then $W \partial \Sigma (W_T,T)$ is dense in the boundary $\partial \Sigma (W,S)$ of the Coxeter system $(W,S)$, where $\partial \Sigma (W_T,T)$ is the boundary of $(W_T,T)$.

References

Martin R. Bridson and André Haefliger, Metric spaces of non-positive curvature, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 319, Springer-Verlag, Berlin, 1999. MR 1744486, DOI 10.1007/978-3-662-12494-9
Michael W. Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. (2) 117 (1983), no. 2, 293–324. MR 690848, DOI 10.2307/2007079
Michael W. Davis, Nonpositive curvature and reflection groups, Handbook of geometric topology, North-Holland, Amsterdam, 2002, pp. 373–422. MR 1886674
Michael W. Davis, The cohomology of a Coxeter group with group ring coefficients, Duke Math. J. 91 (1998), no. 2, 297–314. MR 1600586, DOI 10.1215/S0012-7094-98-09113-X
Tetsuya Hosaka, Parabolic subgroups of finite index in Coxeter groups, J. Pure Appl. Algebra 169 (2002), no. 2-3, 215–227. MR 1897344, DOI 10.1016/S0022-4049(01)00068-8
Tetsuya Hosaka, Dense subsets of the boundary of a Coxeter system, Proc. Amer. Math. Soc. 132 (2004), no. 11, 3441–3448. MR 2073322, DOI 10.1090/S0002-9939-04-07480-5
G. Moussong, Hyperbolic Coxeter groups, Ph.D. thesis, The Ohio State University, 1988.