### Abstract

Let Mod (∑_{g,p}) be the mapping class group of a closed oriented surface ∑_{g,p} of genus g ≥1 with p punctures. Wajnryb proved that Mod(∑_{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 Mod(∑_{g,1}). For p ≥ 2, we prove that Mod(∑_{g,p}) is generated by three elements.

Original language | English |
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Pages (from-to) | 1-9 |

Number of pages | 9 |

Journal | Hiroshima Mathematical Journal |

Volume | 41 |

Issue number | 1 |

Publication status | Published - Mar 1 2011 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory
- Geometry and Topology

### Cite this

**The mapping class group of a punctured surface is generated by three elements.** / Monden, Naoyuki.

Research output: Contribution to journal › Article

*Hiroshima Mathematical Journal*, vol. 41, no. 1, pp. 1-9.

}

TY - JOUR

T1 - The mapping class group of a punctured surface is generated by three elements

AU - Monden, Naoyuki

PY - 2011/3/1

Y1 - 2011/3/1

N2 - Let Mod (∑g,p) be the mapping class group of a closed oriented surface ∑g,p of genus g ≥1 with p punctures. Wajnryb proved that Mod(∑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 Mod(∑g,1). For p ≥ 2, we prove that Mod(∑g,p) is generated by three elements.

AB - Let Mod (∑g,p) be the mapping class group of a closed oriented surface ∑g,p of genus g ≥1 with p punctures. Wajnryb proved that Mod(∑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 Mod(∑g,1). For p ≥ 2, we prove that Mod(∑g,p) is generated by three elements.

UR - http://www.scopus.com/inward/record.url?scp=79953765889&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79953765889&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:79953765889

VL - 41

SP - 1

EP - 9

JO - Hiroshima Mathematical Journal

JF - Hiroshima Mathematical Journal

SN - 0018-2079

IS - 1

ER -