Generating the mapping class groups by torsions

Xiaoming Du

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arXiv · 1506.04396

Generating the mapping class groups by torsions

Xiaoming Du

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Abstract

Let $S_g$ be the closed oriented surface of genus g and let $\text{Mod}(S_g)$ be the mapping class group. When the genus is at least 3, $\text{Mod}(S_g)$ can be generated by torsion elements. We prove the follow results. For $g \geq 4$, $\text{Mod}(S_g)$ can be generated by 4 torsion elements. Three generators are involutions and the forth one is an order 3 element. $\text{Mod}(S_3)$ can be generated by 5 torsion elements. Four generators are involutions and the fifth one is an order 3 element.

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BibTeX RIS

Xiaoming Du. 2015-06-14. Generating the mapping class groups by torsions. https://arxiv.org/abs/1506.04396

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