Groups with a finite Busemann boundary are virtually cyclic
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917106399838208 |
|---|---|
| author | Bodart, Corentin Ron-George, Liran Yadin, Ariel |
| author_facet | Bodart, Corentin Ron-George, Liran Yadin, Ariel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20495 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Groups with a finite Busemann boundary are virtually cyclic Bodart, Corentin Ron-George, Liran Yadin, Ariel Group Theory Metric Geometry 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. |
| title | Groups with a finite Busemann boundary are virtually cyclic |
| topic | Group Theory Metric Geometry |
| url | https://arxiv.org/abs/2511.20495 |