English

Generating the mapping class group of a nonorientable surface by three torsions

Geometric Topology 2020-07-06 v1

Abstract

We prove that the mapping class group M(Ng)\mathcal{M}(N_g) of a closed nonorientable surface of genus gg different than 4 is generated by three torsion elements. Moreover, for every even integer k12k\ge 12 and gg of the form g=pk+2q(k1)g=pk+2q(k-1) or g=pk+2q(k1)+1g=pk+2q(k-1)+1, where p,qp,q are non-negative integers and pp is odd, M(Ng)\mathcal{M}(N_g) is generated by three conjugate elements of order kk. Analogous results are proved for the subgroup of M(Ng)\mathcal{M}(N_g) generated by Dehn twists.

Keywords

Cite

@article{arxiv.2007.01640,
  title  = {Generating the mapping class group of a nonorientable surface by three torsions},
  author = {Marta Leśniak and Błażej Szepietowski},
  journal= {arXiv preprint arXiv:2007.01640},
  year   = {2020}
}

Comments

17 pages, 11 figures

R2 v1 2026-06-23T16:49:41.893Z