论文标题
三个完美的映射课程组
Three perfect mapping class groups
论文作者
论文摘要
我们证明，通过从2个球体，平面或封闭2盘内部卸下插体设置获得的表面的映射类组，没有适当的可计数子组。证明是由曼恩（Mann）建立的这些组的自动连续性的应用。作为推论，我们看到这些组不包含任何适当的有限索子亚组，并且这些组中的每一个都有微不足道的abelianization。
We prove that the mapping class group of a surface obtained from removing a Cantor set from either the 2-sphere, the plane, or the interior of the closed 2-disk has no proper countable-index subgroups. The proof is an application of the automatic continuity of these groups, which was established by Mann. As corollaries, we see that these groups do not contain any proper finite-index subgroups and that each of these groups have trivial abelianization.
