Generating the mapping class groups by torsions

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 $g\ge 4$, $\text{Mod}(S_g)$ 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.

8 pages, 6 figures

References in corpus (3)

• Generating Mapping Class Groups by Involutions
• Torsion Elements in the Mapping Class Group of a Surface
• The extended mapping class group is generated by three symmetries