Simple Connectivity of Spheres in the Curve Complex
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915582024089600 |
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| author | Cao, Richard Prakash, Rishibh |
| author_facet | Cao, Richard Prakash, Rishibh |
| contents | For a fixed radius $r$ and a point $o$ in the curve complex of a surface, we define the sphere of radius $r$ to be the induced subgraph on the set of vertices of distance $r$ from $o$. We show that these spheres are almost simply connected for surfaces of high enough complexity, in the sense that loops in the sphere bound an embedded disk contained in a small neighborhood of the sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23890 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simple Connectivity of Spheres in the Curve Complex Cao, Richard Prakash, Rishibh Geometric Topology 57K20, 20F65 For a fixed radius $r$ and a point $o$ in the curve complex of a surface, we define the sphere of radius $r$ to be the induced subgraph on the set of vertices of distance $r$ from $o$. We show that these spheres are almost simply connected for surfaces of high enough complexity, in the sense that loops in the sphere bound an embedded disk contained in a small neighborhood of the sphere. |
| title | Simple Connectivity of Spheres in the Curve Complex |
| topic | Geometric Topology 57K20, 20F65 |
| url | https://arxiv.org/abs/2510.23890 |