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.
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