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Generating the Mapping Class Group of a Nonorientable Surface by Two Elements or by Three Involutions

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Abstract

We prove that, for \(g\ge 19\) the mapping class group of a nonorientable surface of genus g, \(\mathrm{Mod}(N_g)\), can be generated by two elements, one of which is of order g. We also prove that for \(g\ge 26\), \(\mathrm{Mod}(N_g)\) can be generated by three involutions.

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Acknowledgements

We would like to thank the referee for carefully reading our manuscript and suggesting useful ideas which improved the paper. This work is supported by TÜBİTAK Proj. No. 120F118.

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Authors and Affiliations

  1. Faculty of Engineering, Başkent University, Ankara, Turkey

    Tülіn Altunöz

  2. Department of Mathematics, Middle East Technical University, Ankara, Turkey

    Tülіn Altunöz, Mehmetcіk Pamuk & Oguz Yildiz

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  1. Tülіn Altunöz
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  2. Mehmetcіk Pamuk
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  3. Oguz Yildiz
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Correspondence to Tülіn Altunöz.

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Altunöz, T., Pamuk, M. & Yildiz, O. Generating the Mapping Class Group of a Nonorientable Surface by Two Elements or by Three Involutions. Bull Braz Math Soc, New Series 53, 1145–1156 (2022). https://doi.org/10.1007/s00574-022-00299-4

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  • DOI: https://doi.org/10.1007/s00574-022-00299-4

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