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15
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Every Riemann Surface has a countable basis for its topology

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#general-topology #riemann-surfaces #teichmueller-theory #second-countable
238
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Motivation for Riemann surfaces

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#riemann-surfaces #motivation
120
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Is it a correct definition of the moduli space $\mathcal{M}_{g,n}$ of marked curves?

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#algebraic-geometry #algebraic-curves #riemann-surfaces #moduli-space
768
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Show that $\int_{\partial P}z\frac {f'(z)} {f(z)} dz $ is on the lattice $\Lambda$

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#complex-analysis #differential-geometry #riemann-surfaces
805
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Dirac Operator on Riemann Surface

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#differential-geometry #manifolds #definition #mathematical-physics #riemann-surfaces
193
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Riemann surfaces and folding

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#algebraic-geometry #algebraic-curves #riemann-surfaces #branch-points
129
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Infinite automorphism group implies that Riemann surface is a disk or an annulus?

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#geometry #differential-geometry #riemann-surfaces
100
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Does a $1$-holomorphic form on a Riemann surface induce a metric on that surface?

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#differential-geometry #riemannian-geometry #differential-forms #riemann-surfaces
59
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Equipping topological manifolds with differential/complex structure

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#manifolds #smooth-manifolds #riemann-surfaces
375
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Is the Riemann Sphere a submanifold of $\mathbb{C}^2$?

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#geometry #differential-geometry #manifolds #complex-geometry #riemann-surfaces
1.3k
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Function field and meromorphic functions on a Riemann surface

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#algebraic-geometry #sheaf-theory #riemann-surfaces #meromorphic-functions
58
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How are the following two definitions of holomorphic mappings on Riemann surfaces equivalent?

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#riemann-surfaces
1.9k
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Why compact genus 1 Riemann surface is equivalent to torus?

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#differential-forms #riemann-surfaces #covering-spaces #meromorphic-functions
190
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notation in "Farb & Margalit" 9g-9 theorem

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#algebraic-topology #notation #riemann-surfaces
283
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structural (algebraic) sheaf on a Riemann surface "inside" the sheaf of holomorphic functions

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#algebraic-geometry #manifolds #algebraic-curves #sheaf-theory #riemann-surfaces

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