Finite index subgroups of mapping class groups
Finite index subgroups of mapping class groups
复制标题
映射类群的有限索引子群
DOI：
10.1112/plms/pdt022
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发表时间：
2011
影响因子：
1.8
通讯作者：
Volker Gebhardt
中科院分区：
文献类型：
--
作者：
Luis Paris;Jon A Berrick;Volker Gebhardt
设g⩾3和n⩾0，且ℳg，n是亏格为n个边界分支的曲面的映射类群.证明了ℳg，n包含指数为2g−1(2g−1)至共轭的唯一子群，指数为2g−1(2g+1)至共轭的唯一子群，以及ℳg，n的其它真子群的指数大于2g−1(2g+1).特别地，ℳg，n的真子群的最小指标是2g−1(2g−1)。
Let g⩾3 and n⩾0, and let ℳg, n be the mapping class group of a surface of genus g with n boundary components. We prove that ℳg, n contains a unique subgroup of index 2g−1(2g−1) up to conjugation, a unique subgroup of index 2g−1(2g+1) up to conjugation, and the other proper subgroups of ℳg, n are of index greater than 2g−1(2g+1). In particular, the minimum index for a proper subgroup of ℳg, n is 2g−1(2g−1).