Groups of automorphisms of order 4g acting on non-orientable Riemann surfaces of topological genus g.

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2025年5月26日

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E. Bujalance,
J. J. Etayo,
E. Martínez

摘要

The study of the automorphism groups of surfaces is an important problem. In this paper we find the groups of automorphisms with order 4g acting on non-orientable Riemann surfaces of genus g. In order to get it, we recall a result of Kulkarni on automorphism groups of orientable surfaces of genus $\gamma $ $γ$ , with order greater than $4(\gamma -1)$ $4 (γ - 1)$ . Because he leaves a finite number of cases to be studied, we have completed his work, and then used the relation between the non-orientable Riemann surface Y, and its two-sheeted cover $Y^+$ $Y^{+}$ which is an orientable Riemann surface.