正比例的映射类群元素是伪Anosov
A positive proportion of elements of mapping class groups is pseudo-Anosov
摘要：
在一个闭曲面的映射类群的凯莱图中，对于任何生成集，我们看一个以单位顶点为中心的大半径球，以及这个球中代表伪Anosov元的顶点之间的比例。一个著名的猜想指出，当半径趋于无穷大时，这个比例应该趋于1。我们证明了它保持有界远离零。我们也证明了类似的结果，一个大类的子群的映射类群。
英文摘要：
In the Cayley graph of the mapping class group of a closed surface, with respect to any generating set, we look at a ball of large radius centered on the identity vertex, and at the proportion among the vertices in this ball representing pseudo-Anosov elements. A well-known conjecture states that this proportion should tend to one as the radius tends to infinity. We prove that it stays bounded away from zero. We also prove similar results for a large class of subgroups of the mapping class group.
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。
