Quasi-redirecting boundaries of groups with linear divergence and 3-manifold groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916731508752384 |
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| author | Nguyen, Hoang Thanh |
| author_facet | Nguyen, Hoang Thanh |
| contents | The quasi-redirecting (QR) boundary, introduced by Qing and Rafi, generalizes the Gromov boundary for studying the large-scale geometry of finitely generated groups. Although it is not known to exist for all such groups, its existence has been established for several important classes. We prove that if a finitely generated group G has linear divergence, its QR-boundary is well-defined and consists of a single point. In addition, we show that all finitely generated 3-manifold groups admit well-defined QR-boundaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-redirecting boundaries of groups with linear divergence and 3-manifold groups Nguyen, Hoang Thanh Group Theory The quasi-redirecting (QR) boundary, introduced by Qing and Rafi, generalizes the Gromov boundary for studying the large-scale geometry of finitely generated groups. Although it is not known to exist for all such groups, its existence has been established for several important classes. We prove that if a finitely generated group G has linear divergence, its QR-boundary is well-defined and consists of a single point. In addition, we show that all finitely generated 3-manifold groups admit well-defined QR-boundaries. |
| title | Quasi-redirecting boundaries of groups with linear divergence and 3-manifold groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2505.06790 |