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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:abbreviation
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gptkb:K(G,_n)
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gptkbp:application
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classifying spaces for principal bundles
representing singular cohomology
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gptkbp:category
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CW complexes
topological spaces
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gptkbp:citation
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gptkb:Eilenberg,_S.;_Mac_Lane,_S._(1945)._'Relations_between_homology_and_homotopy_groups_of_spaces.'_Annals_of_Mathematics.
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gptkbp:defines
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A topological space X such that π_n(X) = G and π_k(X) = 0 for all k ≠ n
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gptkbp:example
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K(Z, 1) is the circle S^1
K(G, 0) is a discrete space with fundamental group G
K(Z/2Z, 1) is the infinite real projective space
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gptkbp:field
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gptkb:topology
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https://www.w3.org/2000/01/rdf-schema#label
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Eilenberg–MacLane spaces
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gptkbp:introducedIn
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1940s
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gptkbp:namedAfter
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gptkb:Saunders_Mac_Lane
gptkb:Samuel_Eilenberg
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gptkbp:property
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unique up to homotopy equivalence for given G and n
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gptkbp:relatedConcept
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classifying space
cohomology group
homotopy group
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gptkbp:usedIn
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gptkb:cohomology_theory
homotopy theory
homological algebra
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gptkbp:bfsParent
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gptkb:Homotopy_type_theory
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gptkbp:bfsLayer
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6
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