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Generating the mapping class group of a nonorientable surface by three torsions

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Abstract

We prove that the mapping class group \(\mathcal {M}(N_g)\) of a closed nonorientable surface of genus g different than 4 is generated by three torsion elements. Moreover, for every even integer \(k\ge 12\) and g of the form \(g=pk+2q(k-1)\) or \(g=pk+2q(k-1)+1\), where p, q are non-negative integers and p is odd, \(\mathcal {M}(N_g)\) is generated by three conjugate elements of order k. Analogous results are proved for the subgroup of \(\mathcal {M}(N_g)\) generated by Dehn twists.

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  1. Institute of Mathematics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-308, Gdańsk, Poland

    Marta Leśniak & Błażej Szepietowski

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  1. Marta Leśniak
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  2. Błażej Szepietowski
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Correspondence to Błażej Szepietowski.

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Leśniak, M., Szepietowski, B. Generating the mapping class group of a nonorientable surface by three torsions. Geom Dedicata 216, 40 (2022). https://doi.org/10.1007/s10711-022-00698-3

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