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
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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.
Publié le : 2011-03-15
Classification:  Mapping class group,  punctured surface,  20F65,  57M07 
@article{1301586286,
     author = {Monden, Naoyuki},
     title = {The mapping class group of a punctured surface is generated by three elements},
     journal = {Hiroshima Math. J.},
     volume = {41},
     number = {1},
     year = {2011},
     pages = { 1-9},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1301586286}
}

Monden, Naoyuki. The mapping class group of a punctured surface is generated by three elements. Hiroshima Math. J., Tome 41 (2011) no. 1, pp.  1-9. http://gdmltest.u-ga.fr/item/1301586286/