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