Large-scale geometry of the saddle connection graph

Valentina Disarlo, Huiping Pan, Anja Randecker, Robert Tang

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We prove that the saddle connection graph associated to any halftranslation 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.

Original languageEnglish
Pages (from-to)8101-8129
Number of pages29
JournalTransactions of the American Mathematical Society
Issue number11
Publication statusPublished - Nov 2021


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