Groups with a finite Busemann boundary are virtually cyclic
Abstract
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 .
Fields of Study & Subjects
Geometric and Algebraic Topology
Advanced Operator Algebra Research
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 8
- Publication date
- 24 July 2026
- Language
- EN