THE TWIST SUBGROUP IS GENERATED BY TWO ELEMENTS
Tohoku Mathematical Journal, vol.76, no.2, pp.175-197, 2024 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 76 Issue: 2
- Publication Date: 2024
- Doi Number: 10.2748/tmj.20221017
- Journal Name: Tohoku Mathematical Journal
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Page Numbers: pp.175-197
- Keywords: commutators, generating sets, Mapping class groups, nonorientable surfaces, torsion, twist subgroup
- Middle East Technical University Affiliated: Yes
Abstract
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.