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

preprint2020arXivOpen access

Abstract

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

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