论文标题
关于大型映射课程组的同源
On the homology of big mapping class groups
论文作者
论文摘要
我们证明，单孔第托树表面的映射类组是无环的。反过来，这决定了曾经由曾经的cantor树表面的映射类组的同源性（即平面减去cantor套件），尤其是回答了Calegari和Chen的最新问题。实际上，我们证明了一类称为二进制树表面的一类无限型表面的结果。为了证明我们的结果，我们使用两种主要成分：一种是对与消散组概念有关的马瑟论点的修改；另一个是映射无限型表面类的一般同源稳定性结果。
We prove that the mapping class group of the one-holed Cantor tree surface is acyclic. This in turn determines the homology of the mapping class group of the once-punctured Cantor tree surface (i.e. the plane minus a Cantor set), in particular answering a recent question of Calegari and Chen. We in fact prove these results for a general class of infinite-type surfaces called binary tree surfaces. To prove our results we use two main ingredients: one is a modification of an argument of Mather related to the notion of dissipated groups; the other is a general homological stability result for mapping class groups of infinite-type surfaces.
