Large-scale geometry of the saddle connection graph
We prove that the saddle connection graph associated to any half-translation surface is 4-hyperbolic and uniformly quasi-isometric to the regular countably infinite-valent tree. Consequently, the saddle connection graph is not quasi-isometrically rigid. We also characterise its Gromov boundary as th...
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| Hauptverfasser: | , , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
August 18, 2021
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| In: |
Transactions of the American Mathematical Society
Year: 2021, Jahrgang: 374, Heft: 11, Pages: 8101-8129 |
| ISSN: | 1088-6850 |
| DOI: | 10.1090/tran/8448 |
| Online-Zugang: | Resolving-System, lizenzpflichtig, Volltext: https://doi.org/10.1090/tran/8448 Verlag, lizenzpflichtig, Volltext: https://www.ams.org/tran/2021-374-11/S0002-9947-2021-08448-2/ 
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| Verfasserangaben: | Valentina Disarlo, Huiping Pan, Anja Randecker, and Robert Tang |
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| 520 | |a We prove that the saddle connection graph associated to any half-translation surface is 4-hyperbolic and uniformly quasi-isometric to the regular countably infinite-valent tree. Consequently, the saddle connection graph is not quasi-isometrically rigid. We also characterise its Gromov boundary as the set of straight foliations with no saddle connections. In our arguments, we give a generalisation of the unicorn paths in the arc graph which may be of independent interest. | ||
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