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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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Analytic continuation gives a covering space (and not just a local homeomorphism)

Let $\mathcal{G}$ be the space of germs of holomorphic functions defined on open subsets of $\mathbb{C}$, topologized in the usual way. There is a natural map $p\colon \mathcal{G} \rightarrow \mathbb …
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