Hierarchical hyperbolicity of admissible curve graphs and the boundary of marked strata
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916697196199936 |
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| author | Calderon, Aaron Russell, Jacob |
| author_facet | Calderon, Aaron Russell, Jacob |
| contents | We show that for any surface of genus at least 3 equipped with any choice of framing, the graph of non-separating curves with winding number 0 with respect to the framing is hierarchically hyperbolic but not Gromov hyperbolic. We also describe how to build analogues of the curve graph for marked strata of abelian differentials that capture the combinatorics of their boundaries, analogous to how the curve graph captures the combinatorics of the augmented Teichmueller space. These curve graph analogues are also shown to be hierarchically, but not Gromov, hyperbolic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06798 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hierarchical hyperbolicity of admissible curve graphs and the boundary of marked strata Calderon, Aaron Russell, Jacob Geometric Topology Group Theory 57K20, 20F65, 20F67 We show that for any surface of genus at least 3 equipped with any choice of framing, the graph of non-separating curves with winding number 0 with respect to the framing is hierarchically hyperbolic but not Gromov hyperbolic. We also describe how to build analogues of the curve graph for marked strata of abelian differentials that capture the combinatorics of their boundaries, analogous to how the curve graph captures the combinatorics of the augmented Teichmueller space. These curve graph analogues are also shown to be hierarchically, but not Gromov, hyperbolic. |
| title | Hierarchical hyperbolicity of admissible curve graphs and the boundary of marked strata |
| topic | Geometric Topology Group Theory 57K20, 20F65, 20F67 |
| url | https://arxiv.org/abs/2409.06798 |