## Tokyo Journal of Mathematics

### Generating the Mapping Class Group of a Punctured Surface by Involutions

Naoyuki MONDEN

#### Abstract

Let $\Sigma_{g,b}$ denote a closed oriented surface of genus $g$ with $b$ punctures and let $\mathrm{Mod}(\Sigma_{g,b})$ denote its mapping class group. Kassabov showed that $\mathrm{Mod}(\Sigma_{g,b})$ 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 $\mathrm{Mod}(\Sigma_{g,b})$ is generated by 4 involutions if $g=7$ and $b$ is odd, and 5 involutions if $g=5$ and $b$ is odd.

#### Article information

Source
Tokyo J. Math., Volume 34, Number 2 (2011), 303-312.

Dates
First available in Project Euclid: 30 January 2012

https://projecteuclid.org/euclid.tjm/1327931386

Digital Object Identifier
doi:10.3836/tjm/1327931386

Mathematical Reviews number (MathSciNet)
MR2918906

Zentralblatt MATH identifier
1244.57035

#### Citation

MONDEN, Naoyuki. Generating the Mapping Class Group of a Punctured Surface by Involutions. Tokyo J. Math. 34 (2011), no. 2, 303--312. doi:10.3836/tjm/1327931386. https://projecteuclid.org/euclid.tjm/1327931386

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