Right-angled Coxeter groups with totally disconnected Morse boundaries

TL;DR

This paper introduces a new class of right-angled Coxeter groups with totally disconnected Morse boundaries, constructed via recursive graph gluing and amalgamated free products, expanding understanding of their geometric and boundary properties.

Contribution

It presents a novel recursive construction method for right-angled Coxeter groups with totally disconnected Morse boundaries and a general approach for amalgamated free products of CAT(0) groups.

Findings

Constructed new Coxeter groups with totally disconnected Morse boundaries.

Developed a recursive method for boundary analysis via graph gluing.

Provided a framework for building CAT(0) groups with treelike decompositions.

Abstract

This paper introduces a new class of right-angled Coxeter groups with totally disconnected Morse boundaries. We construct this class recursively by examining how the Morse boundary of a right-angled Coxeter group changes if we glue a graph to its defining graph. More generally, we present a method to construct amalgamated free products of CAT(0) groups with totally disconnected Morse boundaries that act geometrically on CAT(0) spaces that have a treelike block decomposition.