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gptkbp:instanceOf
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gptkb:topology
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gptkbp:abbreviation
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gptkb:K(G,_n)
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gptkbp:category
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gptkb:homotopy_category
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gptkbp:characterizedBy
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π_n(X) = G, π_k(X) = 0 for k ≠ n
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gptkbp:example
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circle S^1 is K(ℤ, 1)
infinite-dimensional complex projective space is K(ℤ, 2)
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gptkbp:fundamentalGroup
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G (if n=1)
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gptkbp:hasApplication
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gptkb:Postnikov_tower
homological algebra
classifying spaces
spectral sequences
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gptkbp:hasProperty
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CW complex
connected if n > 0
simply connected if n > 1
unique up to homotopy equivalence
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gptkbp:homotopyGroup
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π_k = 0 for k ≠ n
π_n = G
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https://www.w3.org/2000/01/rdf-schema#label
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Eilenberg–MacLane space
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gptkbp:introducedIn
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1950s
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gptkbp:namedAfter
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gptkb:Saunders_Mac_Lane
gptkb:Samuel_Eilenberg
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gptkbp:parameter
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group G
integer n
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gptkbp:usedFor
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classifying cohomology classes
representing cohomology functors
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gptkbp:usedIn
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gptkb:topology
gptkb:cohomology_theory
homotopy theory
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gptkbp:bfsParent
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gptkb:Algebraic_topology
gptkb:CW_complex
gptkb:Samuel_Eilenberg
gptkb:Serre's_theorem_on_the_cohomology_of_Eilenberg–MacLane_spaces
gptkb:Kohomologie
gptkb:David_Eilenberg
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gptkbp:bfsLayer
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6
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