Large-scale geometry of the saddle connection graph

• Verfasst von: Disarlo, Valentina [VerfasserIn]
• Verfasst von: Pan, Huiping [VerfasserIn]
• Verfasst von: Randecker, Anja [VerfasserIn]
• Verfasst von: Tang, Robert [VerfasserIn]
• Titel: Large-scale geometry of the saddle connection graph
• Verf.angabe: Valentina Disarlo, Huiping Pan, Anja Randecker, and Robert Tang
• E-Jahr: 2021
• Jahr: August 18, 2021
• Umfang: 29 S.
• Fussnoten: Gesehen am 29.10.2021
• Titel Quelle: Enthalten in: American Mathematical SocietyTransactions of the American Mathematical Society
• Ort Quelle: Providence, RI : Soc., 1900
• Jahr Quelle: 2021
• Band/Heft Quelle: 374(2021), 11, Seite 8101-8129
• ISSN Quelle: 1088-6850
• DOI: doi:10.1090/tran/8448
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1775705099

Abstract

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.