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Addendum to ``Dense subsets of the boundary of a Coxeter system''

Author(s): Tetsuya Hosaka
Journal: Proc. Amer. Math. Soc. 133 (2005), 3745-3747.
MSC (2000): Primary 57M07, 20F65, 20F55
Posted: July 7, 2005
Original article: Proc. Amer. Math. Soc. 132 (2004), 3441-3448.
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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:

1.
M. R. Bridson and A. Haefliger, Metric spaces of non-positive curvature, Springer-Verlag, Berlin, 1999. MR 1744486 (2000k:53038)

2.
M. W. Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. 117 (1983), 293-324. MR 0690848 (86d:57025)

3.
-, Nonpositive curvature and reflection groups, in Handbook of Geometric Topology (Edited by R. J. Daverman and R. B. Sher), pp. 373-422, North-Holland, Amsterdam, 2002. MR 1886674 (2002m:53061)

4.
-, The cohomology of a Coxeter group with group ring coefficients, Duke Math. J. 91 (no.2) (1998), 297-314. MR 1600586 (99b:20067)

5.
T. Hosaka, Parabolic subgroups of finite index in Coxeter groups, J. Pure Appl. Algebra 169 (2002), 215-227. MR 1897344 (2003c:20041)

6.
-, Dense subsets of the boundary of a Coxeter system, Proc. Amer. Math. Soc. 132 (2004), 3441-3448. MR 2073322

7.
G. Moussong, Hyperbolic Coxeter groups, Ph.D. thesis, The Ohio State University, 1988.

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Additional Information:

Tetsuya Hosaka
Affiliation: Department of Mathematics, Utsunomiya University, Utsunomiya, 321-8505, Japan
Email: hosaka@cc.utsunomiya-u.ac.jp

DOI: 10.1090/S0002-9939-05-08307-3
PII: S 0002-9939(05)08307-3
Keywords: Boundaries of Coxeter groups
Received by editor(s): July 5, 2004
Received by editor(s) in revised form: September 12, 2004 and October 5, 2004
Posted: July 7, 2005
Additional Notes: The author was partly supported by the Grant-in-Aid for Scientific Research, The Ministry of Education, Culture, Sports, Science and Technology, Japan (No.~15740029).
Communicated by: Alexander N. Dranishnikov
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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