Quasi-abelian group as automorphism group of Riemann surfaces

Abstract

Conformal/anticonformal actions of the quasi-abelian group $Q{A}_n$ 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 $Q{A}_n$-actions, and for each of these actions, we study the topological rigidity action problem. In the case of pseudo-real surfaces, attention was typically restricted to group actions that admit anticonformal elements. In this paper we consider two cases: either $Q{A}_n$ has anticonformal elements or only contains conformal elements.

arXiv admin note: substantial text overlap with arXiv:2210.01577

Cited by in corpus (1)

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