Parabolic subgroups of Coxeter groups acting by reflections on CAT(0) spaces

Tetsuya Hosaka

Parabolic subgroups of Coxeter groups acting by reflections on CAT(0) spaces

Group Theory 2010-11-30 v2 Geometric Topology

Authors: Tetsuya Hosaka

Abstract

We consider a cocompact discrete reflection group $W$ of a CAT(0) space $X$ . Then $W$ becomes a Coxeter group. In this paper, we study an analogy between the Davis-Moussong complex $\Sigma(W,S)$ and the CAT(0) space $X$ , and show several analogous results about the limit set of a parabolic subgroup of the Coxeter group $W$ .

Keywords

coxeter group cat(0) space reflection group parabolic subgroup davis-moussong complex limit set

Cite

@article{arxiv.math/0409472,
  title  = {Parabolic subgroups of Coxeter groups acting by reflections on CAT(0) spaces},
  author = {Tetsuya Hosaka},
  journal= {arXiv preprint arXiv:math/0409472},
  year   = {2010}
}

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