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

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 $g\ge 3$ and $p\ge 0$.

13 pages, 6 figures

References in corpus (3)

• Presentations for the punctured mapping class groups in terms of Artin groups
• Generating Mapping Class Groups by Involutions
• The extended mapping class group is generated by three symmetries

Cited by in corpus (1)

• Generating the Extended Mapping Class Group by Three Involutions