Hierarchically cocompact classifying spaces for mapping class groups of surfaces CLASSIFYING SPACES FOR MAPPING CLASS GROUPS
Hierarchically cocompact classifying spaces for mapping class groups of surfaces CLASSIFYING SPACES FOR MAPPING CLASS GROUPS
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用于映射曲面类组的层次紧致分类空间 用于映射类组的分类空间
DOI：
10.1112/blms.12166
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发表时间：
2018
影响因子：
0.9
通讯作者：
Nucinkis B
中科院分区：
文献类型：
--
作者：
Nucinkis B
我们为群的子群族定义了层次协紧分类空间的概念。我们的主要应用是证明任何连通的定向紧致曲面的映射类群，可能具有穿孔和边界分量，并具有负欧拉特征，至多具有一个维数虚拟循环子群族的层次协紧模型。当曲面闭合时，我们证明该边界是最优的。特别是，这回答了有关曲面类组映射的 Lück 问题。
We define the notion ofa hierarchically cocompactclassifying space for a family of subgroups of a group. Our main application is to show that the mapping class groupof any connected oriented compact surface, possibly with punctures and boundary components and with negative Euler characteristic has a hierarchically cocompact model for the family of virtually cyclic subgroups of dimension at most. When the surface is closed, we prove that this bound is optimal. In particular, this answers a question of Lück for mapping class groups of surfaces.