论文标题
大型纯制图班级从来都不是完美的
Big pure mapping class groups are never perfect
论文作者
论文摘要
我们表明，无限型表面的紧凑型映射类组的闭合不是完美的，并且其Abelianization包含直接直接直接直接理性总和的直接汇总。我们还将其扩展到Torelli组，并表明在无限属的表面上，Torelli组的Abelianization也包含一个不可分割的免费Abelian组的不可分割的副本。最后，我们通过向理性表现出不连续的同态同态来提出自动连续性问题。
We show that the closure of the compactly supported mapping class group of an infinite type surface is not perfect and that its abelianization contains a direct summand isomorphic to an uncountable direct sum of rationals. We also extend this to the Torelli group and show that in the case of surfaces with infinite genus the abelianization of the Torelli group contains an indivisible copy of an uncountable free abelian group as well. Finally we give an application to the question of automatic continuity by exhibiting discontinuous homomorphisms to the rationals.
