The Extended Mapping Class Group Can Be Generated by Two Torsions

Xiaoming Du

The Extended Mapping Class Group Can Be Generated by Two Torsions

Geometric Topology 2018-02-27 v3 Group Theory

Authors: Xiaoming Du

Abstract

Let $S_g$ be the closed oriented surface of genus g and let $\text{Mod}^{\pm}(S_g)$ be the extended mapping class group of $S_g$ . When the genus is at least 5, we prove that $\text{Mod}^{\pm}(S_g)$ can be generated by two torsion elements. One of these generators is an order 2 element, and the other one is an order 4g+2 element.

Keywords

mapping class groups of surfaces

Cite

@article{arxiv.1607.04030,
  title  = {The Extended Mapping Class Group Can Be Generated by Two Torsions},
  author = {Xiaoming Du},
  journal= {arXiv preprint arXiv:1607.04030},
  year   = {2018}
}

Comments

8 pages, 7 figures. arXiv admin note: text overlap with arXiv:1506.04396

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