论文标题
曲线和弧形的图形图表级别对大型映射类组的图表
Graphs of curves and arcs quasi-isometric to big mapping class groups
论文作者
论文摘要
在Rosendal和Mann和Rafi的工作之后，我们尝试回答以下问题：何时将无限型表面的映射类准级别用于图表，其顶点是该表面上的曲线？在Mann和Rafi定义的驯服性的假设下，我们描述了一个必要且充分的条件，称为转换性，用于几何非平凡的大型映射类组，以承认这种准等级法。此外，我们表明，平面的映射类组减去cantor集合是由Bavard定义的循环图的准图表，我们认为这代表了已知的非元素过高的映射类组的第一个示例。
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.
