On minimal generating sets for the mapping class group of a punctured surface

Naoyuki Monden

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arXiv · 2103.01525

On minimal generating sets for the mapping class group of a punctured surface

Naoyuki Monden

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Abstract

Let $\Sigma_{g,p}$ be a oriented connected surface of genus $g$ with $p$ punctures. We denote by $\mathcal{M}_{g,p}$ and $\mathcal{M}_{g,p}^\pm$ the mapping class group and the extended mapping class group of $\Sigma_{g,p}$, respectively. In this paper, we show that $\mathcal{M}_{g,p}$ and $\mathcal{M}_{g,p}^\pm$ are generated by two element for $g\geq 3$ and $p\geq 0$.

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Naoyuki Monden. 2021-03-02. On minimal generating sets for the mapping class group of a punctured surface. https://arxiv.org/abs/2103.01525

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