Generating the mapping class group of a nonorientable surface by two elements or by three involutions (Q2091183)

From MaRDI portal
scientific article
Language Label Description Also known as
English
Generating the mapping class group of a nonorientable surface by two elements or by three involutions
scientific article

    Statements

    Generating the mapping class group of a nonorientable surface by two elements or by three involutions (English)
    0 references
    0 references
    0 references
    0 references
    31 October 2022
    0 references
    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 \(g \geq 8\).
    0 references
    mapping class groups
    0 references
    nonorientable surfaces
    0 references
    involutions
    0 references

    Identifiers

    0 references
    0 references
    0 references
    0 references
    0 references
    0 references