标题： 几何模型和无限类型曲面映射类群的渐近维数 显示英文标题

标题： Geometric models and asymptotic dimension for infinite-type surface mapping class groups

摘要： 设$S$为一个无限类型曲面，设$G \leq \operatorname{Map}(S)$为一个局部有界波兰子群。 我们构造了一个度量图$M$，它由$S$上的简单弧和曲线组成，并且被$G$的作用所保持，使得顶点轨道映射$G \to V(M)$是一个粗等价；如果$G$是有界生成的，那么$M$是$G$的 Cayley--Abels--Rosendal 图，并且轨道映射是一个拟等距。 特别是，如果$S$包含一个不可位移的子曲面，并且$G \geq \operatorname{PMap}_c(S)$是有界生成的或者$G \in \{\overline{\operatorname{PMap}_c(S)}, \operatorname{PMap}(S), \operatorname{Map}(S) \}$并且是局部有界的，那么$\operatorname{asdim} M = \operatorname{asdim} G = \infty$。 这个结果完成了由 Grant--Rafi--Verberne 开始的稳定有界生成无限类型曲面映射类群的渐近维数分类。 显示英文摘要

摘要： Let $S$ be an infinite-type surface and let $G \leq \operatorname{Map}(S)$ be a locally bounded Polish subgroup. We construct a metric graph $M$ of simple arcs and curves on $S$ preserved by the action of $G$ and for which the vertex orbit map $G \to V(M)$ is a coarse equivalence; if $G$ is boundedly generated, then $M$ is a Cayley--Abels--Rosendal graph for $G$ and the orbit map is a quasi-isometry. In particular, if $S$ contains a non-displaceable subsurface and $G \geq \operatorname{PMap}_c(S)$ is boundedly generated or $G \in \{\overline{\operatorname{PMap}_c(S)}, \operatorname{PMap}(S), \operatorname{Map}(S) \}$ and is locally bounded, then $\operatorname{asdim} M = \operatorname{asdim} G = \infty$. This result completes the classification of the asymptotic dimension of stable boundedly generated infinite-type surface mapping class groups begun by Grant--Rafi--Verberne.