Surprising circles in Morse boundaries of right-angled Coxeter groups

TL;DR

This paper reveals that the Morse boundary of right-angled Coxeter groups can contain embedded circles not associated with Morse Fuchsian subgroups, challenging previous assumptions about the boundary structure.

Contribution

It demonstrates the existence of embedded circles in Morse boundaries that are not derived from Morse Fuchsian subgroups, providing new insights into the boundary topology.

Findings

Morse boundaries can contain non-Fuchsian embedded circles.

Not all embedded circles in Morse boundaries correspond to visible Morse Fuchsian subgroups.

The structure of Morse boundaries in right-angled Coxeter groups is more complex than previously thought.

Abstract

We show that the Morse boundary of a right-angled Coxeter group may contain embedded circles that do not arise as the boundary of a Morse Fuchsian subgroup visible in the defining graph.