Generating the mappingclass groups by torsions
Generating the mappingclass groups by torsions
复制标题
通过扭转生成映射类组
DOI：
10.1142/s0218216517500377
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发表时间：
2017
影响因子：
0.5
通讯作者：
Xiaoming Du
中科院分区：
文献类型：
--
作者：
Xiaoming Du
设S_g$是亏格为g$的闭定向曲面，$Mod（S_g）$是映射类群。当亏格至少为3时，$Mod（S_g）$可由挠元生成.我们证明了如下结果：当g≥4时，Mod（S_g）可以由四个挠元生成.三个生成元是对合，第四个生成元是三阶元。$Mod（S_3）$可以由五个扭转元生成。四个生成元是对合，第五个生成元是三阶元。
Let $S_g$ be a closed oriented surface of genus $g$ and let $Mod(S_g)$ be the mapping class group. When the genus is at least 3, $Mod(S_g)$ can be generated by torsion elements. We prove the following results: For $g≥4$, $Mod(S_g)$ can be generated by four torsion elements. Three generators are involutions and the fourth one is an order three element. $Mod(S_3)$ can be generated by five torsion elements. Four generators are involutions and the fifth one is an order three element.