Geometric characterizations of virtually free groups

TL;DR

This paper establishes that four geometric conditions, stronger than classical hyperbolicity criteria, are equivalent and precisely characterize virtually free groups via their Cayley graphs.

Contribution

It introduces and proves the equivalence of new geometric conditions that characterize virtually free groups in Cayley graphs.

Findings

Four geometric conditions are equivalent in geodesic metric spaces.

These conditions characterize virtually free groups via Cayley graphs.

The conditions are stronger variants of classical hyperbolicity criteria.

Abstract

Four geometric conditions on a geodesic metric space, which are stronger variants of classical conditions characterizing hyperbolicity, are proved to be equivalent. In the particular case of the Cayley graph of a finitely generated group, it is shown that they characterize virtually free groups.