Hiroshima Mathematical Journal

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

Naoyuki Monden

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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.

Article information

Hiroshima Math. J., Volume 41, Number 1 (2011), 1-9.

First available in Project Euclid: 31 March 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 57M07: Topological methods in group theory

Mapping class group punctured surface


Monden, Naoyuki. The mapping class group of a punctured surface is generated by three elements. Hiroshima Math. J. 41 (2011), no. 1, 1--9. doi:10.32917/hmj/1301586286. https://projecteuclid.org/euclid.hmj/1301586286

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