Groups with a finite Busemann boundary are virtually cyclic
Group Theory
2025-11-27 v1 Metric Geometry
Abstract
This note is a continuation of the study of the relationship between the geometry of Cayley graphs and the size of its metric-functional boundary. We show that, if there exists a Cayley graph with finitely many Busemann points, then the underlying group is virtually cyclic. Together with previous works, this completes the full characterization of groups with finite metric-functional boundaries. The main new notion introduced is that of annihilators.
Cite
@article{arxiv.2511.20495,
title = {Groups with a finite Busemann boundary are virtually cyclic},
author = {Corentin Bodart and Liran Ron-George and Ariel Yadin},
journal= {arXiv preprint arXiv:2511.20495},
year = {2025}
}
Comments
17 pages, 3 figures, comments are welcomed