曲线和圆弧拟等距到大映射类群的图
Graphs of curves and arcs quasi-isometric to big mapping class groups
摘要：
继Rosendal，Mann和Rafi的工作之后，我们试图回答这样一个问题：当一个无限型曲面的映射类群与一个顶点为该曲面上曲线的图是拟等距的？在Mann和Rafi定义的驯服性假设下，我们给出了一个几何非平凡的大映射类群允许这种拟等距的充要条件，称为可平移性.此外，我们表明，映射类群的平面减去康托尔集是准等距的Bavard，我们认为代表了第一个例子的一个映射类群被称为非初等双曲定义的循环图。
英文摘要：
Following the work of Rosendal and Mann and Rafi, we try to answer the following question: when is the mapping class group of an infinite-type surface quasi-isometric to a graph whose vertices are curves on that surface? With the assumption of tameness as defined by Mann and Rafi, we describe a necessary and sufficient condition, called translatability, for a geometrically nontrivial big mapping class group to admit such a quasi-isometry. In addition, we show that the mapping class group of the plane minus a Cantor set is quasi-isometric to the loop graph defined by Bavard, which we believe represents the first example of a mapping class group known to be non-elementary hyperbolic.
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