Automorphisms of surface mapping class groups. A recent theorem of N. Ivanov
Automorphisms of surface mapping class groups. A recent theorem of N. Ivanov
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表面映射类组的自同构。
DOI：
10.1007/bf01388732
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发表时间：
1986
影响因子：
3.1
通讯作者：
J. McCarthy
中科院分区：
文献类型：
--
作者：
J. McCarthy
Steklov数学研究所列宁格勒分支的Ivanov证明了曲面映射类群的外自同构群是有限的。本文给出了具有负Euler特征的闭连通可定向曲面的映射类群和扩张映射类群的外自同构群的明确描述。(The扩展映射类群是映射类群通过方向反转合痕类的扩展。对于亏格大于2的曲面，它们分别是二阶循环群和平凡群。对于亏格为2的曲面，它们都是四阶非循环群。(Once同样，亏格2中的超几何对合起着独特的作用。）
SummaryIvanov of the Leningrad Branch of the Steklov Mathematical Institute has shown that the outer automorphism groups of surface mapping class groups are finite. In this report, we shall give explicit descriptions of the outer automorphism groups of both the mapping class groups and extended mapping class groups of closed, connected, orientable surfaces of negative Euler characteristic. (The extended mapping class groups are the extensions of the mapping class groups by the orientation reversing isotopy classes.) For surfaces of genus greater than two, these are, respectively, a cyclic group of order two and the trivial group. For a surface of genus two, these are both noncyclic groups of order four. (Once again, the hypergeometric involution in genus two plays a unique role.)