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7 papers · 1 filter
On boundaries of Coxeter groups and topological fractal structures
Tetsuya Hosaka
In this paper, based on research on rank-one isometries by W.Ballmann and M.Brin and recent research on rank-one isometries of Coxeter groups by P.Caprace and K.Fujiwara, we study…
CAT(0) groups and Coxeter groups whose boundaries are scrambled sets
Tetsuya Hosaka
In this paper, we study CAT(0) groups and Coxeter groups whose boundaries are scrambled sets. Suppose that a group acts geometrically (i.e. properly and cocompactly by isometri…
Minimality of the boundary of a right-angled Coxeter system
Tetsuya Hosaka
In this paper, we show that the boundary of a right-angled Coxeter system is minimal if and only if is irreducible, where i…
Parabolic subgroups of Coxeter groups acting by reflections on CAT(0) spaces
Tetsuya Hosaka
We consider a cocompact discrete reflection group of a CAT(0) space . Then becomes a Coxeter group. In this paper, we study an analogy between the Davis-Moussong complex…
Coxeter systems with two-dimensional Davis-Vinberg complexes
Tetsuya Hosaka
In this paper, we study Coxeter systems with two-dimensional Davis-Vinberg complexes. We show that for a Coxeter group , if and are Coxeter systems with two-dim…
Reflection groups of geodesic spaces and Coxeter groups
Tetsuya Hosaka
H.S.M. Coxeter showed that a group is a finite reflection group of an Euclidean space if and only if is a finite Coxeter group. In this paper, we define {\it reflections} o…