Right-angled Coxeter groups with totally disconnected Morse boundaries

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. We deduce a new proof for the result of Charney-Cordes-Sisto (Complete topological descriptions of certain Morse boundaries, Groups Geom. Dyn. 17(1),157–184 (2023)) that every right-angled Artin group has totally disconnected Morse boundary, and discuss concrete examples of surface amalgams studied by Ben-Zvi (Boundaries of groups with isolated flats are path connected. arXiv:1909.12360, 2019).