On the Involution Generators of the Mapping Class Group of a Punctured Surface

Creative Commons License

ALTUNÖZ T., PAMUK M., Yildiz O.

Mediterranean Journal of Mathematics, vol.20, no.4, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.1007/s00009-023-02439-6
  • Journal Name: Mediterranean Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: generating sets, involutions, Mapping class groups, punctured surfaces
  • Middle East Technical University Affiliated: Yes

Abstract

Let Mod (Σ g,p) denote the mapping class group of a connected orientable surface of genus g with p punctures. For g≥ 14 and even p≥ 10 , we prove that Mod (Σ g,p) can be generated by three involutions. For g≥ 13 and even p≥ 9 , we prove that Mod (Σ g,p) can be generated by four involutions. Moreover, for even p≥ 4 and 3 ≤ g≤ 6 , Mod (Σ g,p) can be generated by four involutions.