Abstract
We prove that for genus $g=3,4$, the extended mapping class group $\text{Mod}^{\pm}(S_g)$ can be generated by two elements of finite orders. But for $g=1$, $\text{Mod}^{\pm}(S_1)$ cannot be generated by two elements of finite orders.
Funding Statement
The author is supported by the Fundamental Research Funds for the Central Universities in China.
Citation
Xiaoming DU. "The torsion generating set of the extended mapping class groups in low genus cases." Osaka J. Math. 58 (4) 815 - 825, October 2021.
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