On boundaries of coxeter groups and topological fractal structures

Abstract

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 a topological fractal structure of boundaries of Coxeter groups. We also show that the limit-point set is dense in a boundary of a Coxeter group and introduce some observations on boundaries of CAT(0) groups with rank-one isometries.