On boundaries of Coxeter groups and topological fractal structures

TL;DR

This paper investigates the fractal structures of Coxeter group boundaries, demonstrating the density of limit points and discussing implications for CAT(0) groups with rank-one isometries.

Contribution

It introduces new insights into the topological fractal structures of Coxeter group boundaries, extending previous work on rank-one isometries.

Findings

Limit-point set is dense in Coxeter group boundaries

Fractal structures are present in the boundaries

Remarks on boundaries of CAT(0) groups with rank-one isometries

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 remarks on boundaries of CAT(0) groups with rank-one isometries.