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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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gptkb:quantum_field_theory
gptkb:Number_theory
gptkb:Topology
gptkb:Algebraic_geometry
gptkb:string_theory
Mathematical physics
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gptkbp:class
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By conformal structure
By genus
By topological type
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gptkbp:defines
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One-dimensional complex manifolds
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gptkbp:dimensions
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1 (complex dimension)
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gptkbp:example
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gptkb:Riemann_sphere
gptkb:Torus
gptkb:Complex_plane
Hyperelliptic curve
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gptkbp:field
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gptkb:Algebraic_geometry
gptkb:Differential_geometry
Complex analysis
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gptkbp:firstDescribed
|
gptkb:Bernhard_Riemann
1851
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https://www.w3.org/2000/01/rdf-schema#label
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Riemann Surfaces
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gptkbp:namedAfter
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gptkb:Bernhard_Riemann
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gptkbp:notable_for
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gptkb:Abel's_theorem
gptkb:Riemann–Roch_theorem
gptkb:Uniformization_theorem
gptkb:Riemann_mapping_theorem
gptkb:Hurwitz's_automorphism_theorem
gptkb:Hodge_theorem
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gptkbp:property
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Can be classified by genus
Locally homeomorphic to open subsets of the complex plane
Can be compact or non-compact
Can be orientable
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gptkbp:relatedTo
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gptkb:Algebraic_curves
gptkb:Uniformization_theorem
gptkb:Sheaf_theory
gptkb:Fundamental_group
Holomorphic functions
Meromorphic functions
Covering spaces
Moduli space of curves
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gptkbp:structure
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gptkb:Riemannian_manifold
Complex structure
Conformal structure
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gptkbp:studiedBy
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gptkb:Felix_Klein
gptkb:Henri_Poincaré
gptkb:Lars_Ahlfors
gptkb:Oswald_Teichmüller
gptkb:Bernhard_Riemann
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gptkbp:usedIn
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gptkb:Algebraic_curves
gptkb:string_theory
gptkb:Teichmüller_theory
Theory of analytic functions
Moduli spaces
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gptkbp:bfsParent
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gptkb:Conformal_Mapping
gptkb:Elliptic_Functions
gptkb:Meromorphic_Functions
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gptkbp:bfsLayer
|
7
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