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

Abstract

Let ${\Sigma }_{g,p}$ be a closed oriented surface of genus $g\ge 1$ with $p$ punctures. Let $\mathrm{Mod}({\mathrm{\Sigma }}_{\text{g,p}})$ be the mapping class group of ${\Sigma }_{g,p}$. Wajnryb proved in [Wa] that for $p=0,1$ $\mathrm{Mod}({\mathrm{\Sigma }}_{\text{g,p}})$ is generated by two elements. Korkmaz proved in [Ko] that one of these generators can be taken as a Dehn twist. For $p\ge 2$, We proved that $\mathrm{Mod}({\mathrm{\Sigma }}_{\text{g,p}})$ is generated by three elements.

7 pages, 5 figures

References in corpus (1)

• Generating Mapping Class Groups by Involutions