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gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:appliesTo
|
Smooth manifolds
|
|
gptkbp:basisFor
|
Closed differential forms modulo exact forms
|
|
gptkbp:degree
|
Non-negative integer
|
|
gptkbp:describes
|
Cohomology of differential forms on manifolds
|
|
gptkbp:field
|
gptkb:Algebraic_topology
gptkb:Differential_geometry
|
|
gptkbp:firstDefined
|
1931
|
|
gptkbp:generalizes
|
gptkb:Sheaf_cohomology
Algebraic de Rham cohomology
|
|
gptkbp:hasApplication
|
gptkb:Algebraic_topology
gptkb:Index_theory
gptkb:gauge_theory
gptkb:Electromagnetism
gptkb:Mathematical_analysis
gptkb:string_theory
Characteristic classes
Topology of manifolds
|
|
gptkbp:hasInvariant
|
Smooth manifold
|
|
gptkbp:heldBy
|
Functor from category of smooth manifolds to graded vector spaces
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
De Rham Cohomology
|
|
gptkbp:importantFor
|
gptkb:Hodge_theory
gptkb:Algebraic_geometry
gptkb:Morse_theory
Mathematical physics
|
|
gptkbp:isomorphismWith
|
Singular cohomology with real coefficients
|
|
gptkbp:namedAfter
|
gptkb:Georges_de_Rham
|
|
gptkbp:output
|
Graded vector space
|
|
gptkbp:relatedTo
|
gptkb:de_Rham_theorem
gptkb:Poincaré_lemma
gptkb:Singular_cohomology
|
|
gptkbp:usedFor
|
Classifying topological properties of manifolds
|
|
gptkbp:uses
|
Differential forms
Exterior derivative
|
|
gptkbp:bfsParent
|
gptkb:Singular_Homology_Theory
|
|
gptkbp:bfsLayer
|
7
|