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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:canBe
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modules
abelian groups
|
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gptkbp:capturedBy
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topological invariants
|
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gptkbp:defines
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simplicial complexes
topological spaces
chain complexes
|
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gptkbp:field
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gptkb:topology
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gptkbp:firstAppearance
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early 20th century
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gptkbp:generalizes
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gptkb:cohomology_theory
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https://www.w3.org/2000/01/rdf-schema#label
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Homology groups
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gptkbp:introduced
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gptkb:Henri_Poincaré
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gptkbp:notation
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H^n(X)
H_n(X)
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gptkbp:relatedTo
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gptkb:Betti_numbers
boundaries
cycles
cohomology groups
chain complexes
|
|
gptkbp:used_in
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gptkb:algebraic_geometry
gptkb:topology
gptkb:universal_coefficient_theorem
gptkb:K-theory
gptkb:Poincaré_duality
gptkb:algebraic_K-theory
gptkb:Morse_theory
gptkb:category_theory
gptkb:Künneth_theorem
gptkb:persistent_homology
gptkb:de_Rham_cohomology
differential topology
homotopy theory
homological algebra
intersection theory
algebraic cycles
bordism theory
cellular homology
group cohomology
sheaf cohomology
simplicial homology
spectral sequences
functoriality
derived categories
exact sequences
singular homology
homological mirror symmetry
spectral homology
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gptkbp:used_to_compute
|
holes in spaces
|
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gptkbp:used_to_distinguish
|
topological spaces
|
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gptkbp:bfsParent
|
gptkb:Betti_Numbers
gptkb:Cellular_Homology
gptkb:Simplicial_Complexes
|
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gptkbp:bfsLayer
|
8
|