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March 2011 The mapping class group of a punctured surface is generated by three elements
Naoyuki Monden
Hiroshima Math. J. 41(1): 1-9 (March 2011). DOI: 10.32917/hmj/1301586286

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.

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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

Information

Published: March 2011
First available in Project Euclid: 31 March 2011

zbMATH: 1229.57001
MathSciNet: MR2809044
Digital Object Identifier: 10.32917/hmj/1301586286

Subjects:
Primary: 20F65
Secondary: 57M07

Rights: Copyright © 2011 Hiroshima University, Mathematics Program

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Vol.41 • No. 1 • March 2011
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