Abstract
Conformal/anticonformal actions of the quasi-abelian group \(QA_{n}\) of order \(2^n\), for \(n\ge 4\), on closed Riemann surfaces, pseudo-real Riemann surfaces and closed Klein surfaces are considered. We obtain several consequences, such as the solution of the minimum genus problem for the \(QA_n\)-actions, and for each of these actions, we study the topological rigidity action problem. In the case of pseudo-real Riemann surfaces, attention was typically restricted to group actions that admit anticonformal elements. In this paper, we consider two cases: either \(QA_n\) has anticonformal elements or only contains conformal elements.
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The authors would like to thank the referees for their effort in reviewing this paper and for the provided suggestions, comments, and corrections. The results of this article are mostly based on the second author’s Ph.D. thesis.
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Partially supported by Projects FONDECYT Regular N. 1220261 and 1230001. The second author has been supported by ANID/Beca de Doctorado Nacional/ 21190335.
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Hidalgo, R.A., Marín Montilla, Y.L. & Quispe, S. Quasi-abelian group as automorphism group of Riemann surfaces. manuscripta math. (2024). https://doi.org/10.1007/s00229-024-01552-4
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DOI: https://doi.org/10.1007/s00229-024-01552-4