Generating the mapping class group of a nonorientable surface by two elements or by three involutions (Q2091183)
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| Language | Label | Description | Also known as |
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| English | Generating the mapping class group of a nonorientable surface by two elements or by three involutions |
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Generating the mapping class group of a nonorientable surface by two elements or by three involutions (English)
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31 October 2022
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Let \(N_g\) be the closed connected non-orientable surface of genus \(g\). Let \(\mathrm{Mod}(N_g)\) be the mapping class group of \(N_g\). In the present paper, the authors show that for \(g \geq 19\), \(\mathrm{Mod}(N_g)\) is generated by two elements, where one of the elements is of order \(g\). In addition to this, it is also shown that for \(g \geq 26\), \(\mathrm{Mod}(N_g)\) is generated by three involutions (order two elements). An analogous result has been obtained by \textit{M. Korkmaz} [Math. Res. Lett. 27, No. 4, 1095--1108 (2020; Zbl 1459.57020)] for closed orientable surfaces of genus \(g \geq 8\).
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mapping class groups
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nonorientable surfaces
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involutions
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