Generating the mapping class groups by torsions

被引：3

作者：

Du, Xiaoming ^{[1
]}

机构：

[1] South China Univ Technol, Sch Math, Guangzhou 510640, Guangdong, Peoples R China

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2017年 / 26卷 / 07期

关键词：

Mapping class group; generator; torsion; involution; FINITE-SET; 2; ELEMENTS; SURFACE;

D O I：

10.1142/S0218216517500377

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：8

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