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- W3136343255 abstract "In 1963, Greenberg proved that every finite group appears as the monodromy group of some morphism of Riemann surfaces. In this paper, we give two constructive proofs of Greenberg's result. First, we utilize free groups, which given with the universal property and their construction as discrete subgroups of $operatorname{PSL}_2(mathbb{R})$, yield a very natural realization of finite groups as monodromy groups. We also give a proof of Greenberg's result based on triangle groups $Delta(m, n, k)$. Given any finite group $G$, we make use of subgroups of $Delta(m, n, k)$ in order to explicitly find a morphism $pi$ such that $G simeq operatorname{Mon}(pi)$." @default.
- W3136343255 created "2021-03-29" @default.
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- W3136343255 date "2021-03-18" @default.
- W3136343255 modified "2023-09-27" @default.
- W3136343255 title "Explicit Constructions of Finite Groups as Monodromy Groups" @default.
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- W3136343255 hasPublicationYear "2021" @default.
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