Morse boundaries of graphs of groups with finite edge groups

TL;DR

This paper demonstrates that the Morse boundary of certain complex groups, specifically graphs of groups with finite edge groups, can be determined solely from the Morse boundaries of their component groups, extending previous results.

Contribution

It generalizes the understanding of Morse boundaries from free products to graphs of groups with finite edge groups and infinitely many ends.

Findings

Morse boundary of a free product depends only on its factors' Morse boundaries

Extension of results to graphs of groups with finite edge groups and infinitely many ends

Generalization of Martin-Swiatkowski's result to non-hyperbolic groups

Abstract

In this paper we prove that the Morse boundary of a free product depends only on the Morse boundary of its factors. In fact, we also prove the analogous result for graphs of groups with finite edge groups and infinitely many ends. This is a generalization of a result of Martin-Swiatkowski in the case of non-hyperbolic groups.