The arc complex is not quasi-isometric to the sphere complex
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908490708025344 |
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| author | Aougab, Tarik Loving, Marissa |
| author_facet | Aougab, Tarik Loving, Marissa |
| contents | We show that the arc complex $\mathcal{A}(S_{g,1})$ is not quasi-isometric to the sphere complex $\mathcal S_{2g}$ associated to the double of a genus $2g$ handlebody. Along the way, we present a simple proof that $\mathcal{A}(S_{g,1})$ is quasi-isometrically rigid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11065 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The arc complex is not quasi-isometric to the sphere complex Aougab, Tarik Loving, Marissa Geometric Topology Group Theory 57K20 We show that the arc complex $\mathcal{A}(S_{g,1})$ is not quasi-isometric to the sphere complex $\mathcal S_{2g}$ associated to the double of a genus $2g$ handlebody. Along the way, we present a simple proof that $\mathcal{A}(S_{g,1})$ is quasi-isometrically rigid. |
| title | The arc complex is not quasi-isometric to the sphere complex |
| topic | Geometric Topology Group Theory 57K20 |
| url | https://arxiv.org/abs/2508.11065 |