The mapping class group of a punctured surface is generated by three elements

Monden, Naoyuki

Hiroshima Math. J., Tome 41 (2011) no. 1, p. 1-9 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2011-03-15
Classification:  Mapping class group,  punctured surface,  20F65,  57M07