斑点圆盘图与球面图
Spotted disk and sphere graphs
AI总结：
本文研究带标记点柄体的圆盘图及双柄体球面图的大尺度几何，证明二者分别包含拟等距嵌入的 ℝ² 与任意维 ℝⁿ 副本。
摘要：
亏格 g≥2、边界上带有 m≥0 个标记点的柄体 H 的圆盘图，是这样一个图：其顶点为避开标记点的圆盘的同痕类，若两个顶点可实现为互不相交，则由一条长度为一的边相连。我们证明，当 m=2 时，该圆盘图包含拟等距嵌入的 ℝ² 副本。此外，亏格 g≥4、带有两个标记点的双柄体的球面图，对每个 n≥1 都包含一个拟等距嵌入的 ℝⁿ 副本。
英文摘要：
The disk graph of a handlebody H of gneus $g\geq 2$ with $m\geq 0$ marked points on the boundary is the graph whose vertices are isotopy classes of disks disjoint from the marked points and where two vertices are connected by an edge of length one if they can be realized disjointly. We show that for m=2 the disk graph contains quasi-isometrically embedded copies of $\mathbb{R}^2$. Furthermore, the sphere graph of the doubled handlebody of genus $g\geq 4$ with two marked points contains for every $n\geq 1$ a quasi-isometrically embedded copy of $\mathbb{R}^n$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
