论文标题
马鞍连接图的大规模几何形状
Large-scale geometry of the saddle connection graph
论文作者
论文摘要
我们证明，与任何半翻译表面相关的鞍形连接图是4-纤维的，并且与常规的无限无限树相关。因此，马鞍连接图在准静态上不是刚性的。我们还将其Gromov边界描述为没有鞍座连接的一组直叶。在我们的论点中，我们对弧形图中的独角兽路径进行了概括，这可能具有独立的兴趣。
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.
