GENERATING THE EXTENDED MAPPING CLASS GROUP BY THREE INVOLUTIONS

ALTUNOZ T. U. L. I. N., PAMUK M. E. H. M. E. T. C. I. K., YILDIZ O. G. U. Z.

OSAKA JOURNAL OF MATHEMATICS, vol.60, no.1, pp.61-75, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 60 Issue: 1
  • Publication Date: 2023
  • Journal Name: OSAKA JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.61-75
  • Middle East Technical University Affiliated: Yes

Abstract

We prove that the extended mapping class group, Mod*(S-g), of a connected orientable surface of genus g, can be generated by three involutions for g = 5. In the presence of punctures, we prove that Mod*(S-g,S-p) can be generated by three involutions for g =10 and p = 6 (with the exception that for g = 11, p should be at least 15).