The Torsion Generating Set Of The Extended Mapping Class Groups In Low Genus Cases

Abstract

We prove that for genus $g=3,4$, the extended mapping class group ${\text{Mod}}^{\pm }(S_g)$ can be generated by two elements of finite orders. But for $g=1$, ${\text{Mod}}^{\pm }(S_1)$ cannot be generated by two elements of finite orders.

10 pages, 14 figures