English

Torsion normal generators of the mapping class group of a non-orientable surface

Geometric Topology 2019-03-26 v1

Abstract

We show that the normal closure of any periodic element of the mapping class group of a non-orientable surface whose order is greater than 2 contains the commutator subgroup, which for g7g\geq 7 is equal to the twist subgroup, and provide necessary and sufficient conditions for the normal closures of involutions to contain the twist subgroup. Finally, we provide a criterion for a periodic element to normally generate M(Ng)\mathcal{M}(N_g) and give examples.

Keywords

Cite

@article{arxiv.1903.10285,
  title  = {Torsion normal generators of the mapping class group of a non-orientable surface},
  author = {Marta Leśniak},
  journal= {arXiv preprint arXiv:1903.10285},
  year   = {2019}
}

Comments

33 pages, 29 figures