Abstract
Let $\rm Mod(\Sigma_{\textit{g,p}})$ be the mapping class group of a closed oriented surface $\Sigma_{g,p}$ of genus $g\geq 1$ with $p$ punctures. Wajnryb proved that $\rm Mod({\Sigma_{\textit{g},0}})$ is generated by two elements. Korkmaz proved that one of these generators may be taken to be a Dehn twist. Korkmaz also proved the same result in the case of $\rm Mod(\Sigma_{\textit{g},1})$. For $p\geq 2$, we prove that $\rm Mod(\Sigma_{\textit{g,p}})$ is generated by three elements.
Citation
Naoyuki Monden. "The mapping class group of a punctured surface is generated by three elements." Hiroshima Math. J. 41 (1) 1 - 9, March 2011. https://doi.org/10.32917/hmj/1301586286
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