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| Autori principali: | , , |
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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2511.20495 |
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| _version_ | 1866917106399838208 |
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| 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 |