THE TWIST SUBGROUP IS GENERATED BY TWO ELEMENTS

Altunöz T., Pamuk M., Yildiz O.

Tohoku Mathematical Journal, cilt.76, sa.2, ss.175-197, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 76 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.2748/tmj.20221017
  • Dergi Adı: Tohoku Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.175-197
  • Anahtar Kelimeler: commutators, generating sets, Mapping class groups, nonorientable surfaces, torsion, twist subgroup
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

We show that the twist subgroup Tg of a nonorientable surface of genus g can be generated by two elements for every odd g ≥ 21 and even g ≥ 50. Using these generators, we can also show that Tg can be generated by two or three commutators depending on g modulo 4. Moreover, we show that Tg can be generated by three elements if g ≥ 8. For this general case, the number of commutator generators is either three or four depending on g modulo 4 again.