论文标题
尼尔森实现无限型表面
Nielsen realization for infinite-type surfaces
论文作者
论文摘要
Given a finite subgroup G of the mapping class group of a surface S, the Nielsen realization problem asks whether G can be realized as a finite group of homeomorphisms of S. In 1983, Kerckhoff showed that for S a finite-type surface, any finite subgroup G may be realized as a group of isometries of some hyperbolic metric on S. We extend Kerckhoff's result to orientable,无限型表面。作为应用程序，我们将平面的映射类中的扭转元素分类为减去一个cantor集合，并表明包含限制到身份的扭转元素序列的拓扑组不会连续嵌入S的映射类组。最后，我们显示，S映射类的S映射类小组是有限的，是有限的，是有限的。
Given a finite subgroup G of the mapping class group of a surface S, the Nielsen realization problem asks whether G can be realized as a finite group of homeomorphisms of S. In 1983, Kerckhoff showed that for S a finite-type surface, any finite subgroup G may be realized as a group of isometries of some hyperbolic metric on S. We extend Kerckhoff's result to orientable, infinite-type surfaces. As applications, we classify torsion elements in the mapping class group of the plane minus a Cantor set, and also show that topological groups containing sequences of torsion elements limiting to the identity do not embed continuously into the mapping class group of S. Finally, we show that compact subgroups of the mapping class group of S are finite, and locally compact subgroups are discrete.
