An infinite family of exotic subgroups of hyperbolic groups
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913317543477248 |
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| author | Kudlinska, Monika |
| author_facet | Kudlinska, Monika |
| contents | We construct the first known infinite family of quasi-isometry classes of subgroups of hyperbolic groups which are not hyperbolic and are of type $\mathrm{FP}(\mathbb{Q})$. We give a simple criterion for producing many non-hyperbolic subgroups of hyperbolic groups with strong finiteness properties. We also observe that local hyperbolicity and algebraic fibring are mutually exclusive in higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11218 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An infinite family of exotic subgroups of hyperbolic groups Kudlinska, Monika Group Theory Primary 20F67, Secondary 20E07, 20J05, 57M07 We construct the first known infinite family of quasi-isometry classes of subgroups of hyperbolic groups which are not hyperbolic and are of type $\mathrm{FP}(\mathbb{Q})$. We give a simple criterion for producing many non-hyperbolic subgroups of hyperbolic groups with strong finiteness properties. We also observe that local hyperbolicity and algebraic fibring are mutually exclusive in higher dimensions. |
| title | An infinite family of exotic subgroups of hyperbolic groups |
| topic | Group Theory Primary 20F67, Secondary 20E07, 20J05, 57M07 |
| url | https://arxiv.org/abs/2303.11218 |