Large-scale geometry of the saddle connection graph
Large-scale geometry of the saddle connection graph
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DOI：
10.1090/tran/8448
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Robert Tang
中科院分区：
文献类型：
--
作者：
Valentina Disarlo;Huiping Pan;Anja Randecker;Robert Tang
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.
