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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.

5 votes
3 answers
487 views

Unramified map of Riemann surfaces

Let $f:S \to T$ be a surjective, unramified, holomorphic map between connected Riemann surfaces. If $S$ is not compact is it always true that $f$ is a covering? This is of course true if $S$ is compa …
4 votes
1 answer
274 views

Reference for Teichmuller spaces of punctured surfaces

What is a good reference for Teichmuller spaces of punctured surfaces $S_{g,n}$ where $n>0$? I am looking for a reference where there is the correct statement and or proof of say the Bers embedding, R …
5 votes
1 answer
939 views

Mapping class group of a punctured genus 0 surface

Let $T_{0,n}$ be the Teichmuller space of $n$-punctured genus $0$ Riemann surface, and $M_{0,n}$ the Moduli space (assume $n\geq 3$ and the punctures are numbered). What is the correct notion of the m …