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Generating the mapping class group of a non-orientable punctured surface by involutions

2022/12/20 by Kazuya Yoshihara, Yoshihara, Kazuya · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2212.09924

openalex publication_date 2022/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ng,n denote the closed non-orientable surface of genus g with n punctures and let \mathcal Ng,n denote the mapping class group of Ng,n. Szepietowski showed that \mathcal Ng,n is generated by finitely many involutions. The number of elements in his generating set depends linearly on g and n. In the case of n=0, Szepietowski found an involution generating set in such a way that the number of its elements does not depend on g, showing that \mathcal Ng,0 is generated by four involutions. In this thesis, for n ≥ 0, we prove that \mathcal Ng,n is generated by eight involutions if g ≥ 13 is odd and by eleven involutions if g ≥ 14 is even.

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