Tokyo Journal of Mathematics

Generating the Mapping Class Group of a Punctured Surface by Involutions

Naoyuki MONDEN

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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

Permanent link to this document
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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References

  • T. E. Brendle and B. Farb, Every mapping class group is generated by 3 torsion elements and by 6 involutions, J. Algebra, 278 (2004), 187–198.
  • S. Gervais, A finite presentation of the mapping class group of a punctured surface, Topology, 40 (2001), No. 4, 703–725.
  • M. Kassabov, Generating Mapping Class Groups by Involutions. v1 25 Nov, 2003.
  • N. Lu, On the mapping class groups of the closed orientable surfaces, Topology Proc., 13 (1988), 293–324.
  • J. MacCarthy and A. Papadopoulos, Involutions in surface mapping class groups, Enseign. Math., 33 (1987), 275–290.