Quasi-abelian group as automorphism group of Riemann surfaces

期刊论文
发表日期：

2024年4月3日

查看全文

Rubén A. Hidalgo,
Yerika L. Marín Montilla,
Saúl Quispe

摘要

Conformal/anticonformal actions of the quasi-abelian group $QA_{n}$ $Q A_{n}$ of order $2^n$ $2^{n}$ , for $n\ge 4$ $n \geq 4$ , 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 $QA_n$ $Q A_{n}$ -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 $QA_n$ $Q A_{n}$ has anticonformal elements or only contains conformal elements.