English

On the Torsion Generators of the Mapping Class Groups

Geometric Topology 2023-12-08 v1

Abstract

We study torsion generators for the (extended) mapping class group or the extended mapping class group of a closed connected orientable surface of genus g. We show that for every g is grater than or equal to 14, mapping class group can be generated by two torsion elements of order g+1 if g is even, and of orders g+1 and g+1 if g is odd. Also for g grater than or equal to 16, mapping class group can be generated by two torsion elements of orders g+1 if g+1 is not divisible by 3, and of orders g+1 and g+1 if g+1 is divisible by 3. Similarly, we obtain two torsion elements generating extended mapping class groups.

Keywords

Cite

@article{arxiv.2312.04058,
  title  = {On the Torsion Generators of the Mapping Class Groups},
  author = {Tulin Altunoz and Mehmetcik Pamuk and Oguz Yildiz},
  journal= {arXiv preprint arXiv:2312.04058},
  year   = {2023}
}

Comments

12 pages, 2 figures. Any comments are welcome

R2 v1 2026-06-28T13:43:38.440Z