Quasi-isometry invariance of hyperbolicity in semimetric spaces, digraphs and semigroups
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866913258837901312 |
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| author | Hamann, Matthias |
| author_facet | Hamann, Matthias |
| contents | Gray and Kambites introduced a notion of hyperbolicity in the setting of semimetric spaces like digraphs or semigroups. We will prove that under a small additional geometric assumption their notion of hyperbolicity is preserved by quasi-isometries. Applied to semigroups, this will partially solve a problem of Gray and Kambites. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_13049 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Quasi-isometry invariance of hyperbolicity in semimetric spaces, digraphs and semigroups Hamann, Matthias Metric Geometry Combinatorics Group Theory Gray and Kambites introduced a notion of hyperbolicity in the setting of semimetric spaces like digraphs or semigroups. We will prove that under a small additional geometric assumption their notion of hyperbolicity is preserved by quasi-isometries. Applied to semigroups, this will partially solve a problem of Gray and Kambites. |
| title | Quasi-isometry invariance of hyperbolicity in semimetric spaces, digraphs and semigroups |
| topic | Metric Geometry Combinatorics Group Theory |
| url | https://arxiv.org/abs/2110.13049 |