Let $\Sigma_{ g,p}$ be a closed oriented surface of genus $g\geq 1$ with $p$ punctures. Let $\rm Mod(\Sigma_{ \textit{ g,p}})$ be the mapping class group of $\Sigma_{ g,p}$. Wajnryb proved in [Wa] that for $p=0, 1$ $\rm Mod({ \Sigma_{ \textit{ g,p}}})$ is generated by two elements. Korkmaz proved in [Ko] that one of these generators can be taken as a Dehn twist. For $p\geq 2$, We proved that $\rm Mod(\Sigma_{ \textit{ g,p}})$ is generated by three elements.
Categories: math.GT math.GR