### Abstract

Let Σ_{g, b} denote a closed oriented surface of genus g with b punctures and let Mod(Σ_{g, b}) denote its mapping class group. Kassabov showed that Mod(Σ_{g, b}) is generated by 4 involutions if g > 7 or g = 7 and b is even, 5 involutions if g > 5 or g = 5 and b is even, and 6 involutions if g > 3 or g = 3 and b is even. We proved that Mod(Σ_{g, b}) is generated by 4 involutions if g = 7 and b is odd, and 5 involutions if g = 5 and b is odd.

Original language | English |
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Pages (from-to) | 303-312 |

Number of pages | 10 |

Journal | Tokyo Journal of Mathematics |

Volume | 34 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 2017 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Generating the mapping class group of a punctured surface by involutions.** / Monden, Naoyuki.

Research output: Contribution to journal › Article

*Tokyo Journal of Mathematics*, vol. 34, no. 2, pp. 303-312. https://doi.org/10.3836/tjm/1327931386

}

TY - JOUR

T1 - Generating the mapping class group of a punctured surface by involutions

AU - Monden, Naoyuki

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Let Σg, b denote a closed oriented surface of genus g with b punctures and let Mod(Σg, b) denote its mapping class group. Kassabov showed that Mod(Σg, b) is generated by 4 involutions if g > 7 or g = 7 and b is even, 5 involutions if g > 5 or g = 5 and b is even, and 6 involutions if g > 3 or g = 3 and b is even. We proved that Mod(Σg, b) is generated by 4 involutions if g = 7 and b is odd, and 5 involutions if g = 5 and b is odd.

AB - Let Σg, b denote a closed oriented surface of genus g with b punctures and let Mod(Σg, b) denote its mapping class group. Kassabov showed that Mod(Σg, b) is generated by 4 involutions if g > 7 or g = 7 and b is even, 5 involutions if g > 5 or g = 5 and b is even, and 6 involutions if g > 3 or g = 3 and b is even. We proved that Mod(Σg, b) is generated by 4 involutions if g = 7 and b is odd, and 5 involutions if g = 5 and b is odd.

UR - http://www.scopus.com/inward/record.url?scp=84958949454&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958949454&partnerID=8YFLogxK

U2 - 10.3836/tjm/1327931386

DO - 10.3836/tjm/1327931386

M3 - Article

AN - SCOPUS:84958949454

VL - 34

SP - 303

EP - 312

JO - Tokyo Journal of Mathematics

JF - Tokyo Journal of Mathematics

SN - 0387-3870

IS - 2

ER -