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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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A continuous version of Teichmuller uniqueness
By the Teichmuller uniqueness theorem, given a homeomorphism $f:X \rightarrow X$ where $X$ is the $n$-punctured sphere, there is a unique quasiconformal homeomorphism $g$ fixing $0$, $1$, and $\infty …
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Atiyah-Bott Yang-Mills connections
In Atiyah-Bott's paper on Yang-Mills equations on Riemann surfaces, a special case of what they do is to prove that Unitary Yang-Mills connections over a R.S $M$ are in bijective correspondence with u …