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Riemann surfaces(Riemannian surfaces) is one dimensional complex manifold. For questions about classical examples in complex analysis, complex geometry, surface topology.

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multivalued holomorphic function on Riemann surfaces

Let $M$ be an open Riemann surface and $f$ a multivalued holomorphic function from $M$ to $\mathbb{H}$, where $\mathbb{H}$ is the upper half plane. Suppose that the monodromy of $f$ lies in the two-di …
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