论文标题
Cantor树的映射类组只有几何正常亚组
The mapping class group of the Cantor tree has only geometric normal subgroups
论文作者
论文摘要
如果其自动形态组是映射类组，则表面的（扩展）映射类组的正常亚组被认为是几何的。我们证明，在Cantor树表面，每个正常的亚组都是几何。我们注意到，没有非平凡的有限型映射类组为此。我们研究了曲线图的概括，证明其自动形态组再次是映射类组。该策略是根据Brendle-Margalit和有限型设置中某些正常亚组的作者的改编而来的。
A normal subgroup of the (extended) mapping class group of a surface is said to be geometric if its automorphism group is the mapping class group. We prove that in the case of the Cantor tree surface, every normal subgroup is geometric. We note that there is no non-trivial finite-type mapping class group for which this statement is true. We study a generalisation of the curve graph, proving that its automorphism group is again the mapping class group. This strategy is adapted from that of Brendle-Margalit and the author for certain normal subgroups in the finite-type setting.
