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

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

2008-10-06

arxiv.org/abs/0810.0984v1

Mathematics

Geometric Topology

7 pages, 5 figures

Scientific paper

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.

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