Spheres in the curve graph and linear connectivity of the Gromov boundary
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866917741504495616 |
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| author | Wright, Alex |
| author_facet | Wright, Alex |
| contents | We consider the curve graph in the cases where it is not a Farey graph, and show that its Gromov boundary is linearly connected. For a fixed center point c and radius r, we define the sphere of radius r to be the induced subgraph on the set of vertices of distance r from c. We show that these spheres are always connected in high enough complexity, and prove a slightly weaker result for low complexity surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03004 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spheres in the curve graph and linear connectivity of the Gromov boundary Wright, Alex Geometric Topology We consider the curve graph in the cases where it is not a Farey graph, and show that its Gromov boundary is linearly connected. For a fixed center point c and radius r, we define the sphere of radius r to be the induced subgraph on the set of vertices of distance r from c. We show that these spheres are always connected in high enough complexity, and prove a slightly weaker result for low complexity surfaces. |
| title | Spheres in the curve graph and linear connectivity of the Gromov boundary |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2304.03004 |