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

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ALTUNÖZ T., PAMUK M., Yildiz O.

Mediterranean Journal of Mathematics, cilt.20, sa.4, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 4
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s00009-023-02439-6
  • Dergi Adı: Mediterranean Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: generating sets, involutions, Mapping class groups, punctured surfaces
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.