Abstract
We prove that the extended mapping class group, $\mod^{*}(\Sigma_{g})$, of a connected orientable surface of genus $g$, can be generated by three involutions for $g\geq 5$. In the presence of punctures, we prove that $\mod^{*}(\Sigma_{g,p})$ can be generated by three involutions for $g\geq 10$ and $p\geq 6$ (with the exception that for $g\geq 11$, $p$ should be at least $15$).
Acknowledgments
We would like to thank Tara Brendle for her helpful comments. We also would like to thank the referee for carefully reading our manuscript, pointing out an error in an earlier version and suggesting useful ideas which improved the paper.
The first author was partially supported by the Scientific and Technological Research Council of Turkey (TÜ Bİ TAK)[grant number 117F015].
Citation
Tülin Altunöz. Mehmetcik Pamuk. Oğuz Yildiz. "Generating the Extended Mapping Class Group by Three Involutions." Osaka J. Math. 60 (1) 61 - 75, January 2023.
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