Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:topology
|
| gptkbp:abbreviation |
gptkb:K(G,_n)
|
| gptkbp:category |
gptkb:homotopy_category
|
| gptkbp:citation |
gptkb:Eilenberg,_S.;_Mac_Lane,_S._(1945)._"Relations_between_homology_and_homotopy_groups_of_spaces"._Annals_of_Mathematics.
|
| gptkbp:definedIn |
group G and integer n ≥ 1
|
| gptkbp:example |
K(ℤ, 2) is the infinite-dimensional complex projective space
K(ℤ, 1) is the circle S^1 K(ℤ/2ℤ, 1) is the infinite real projective space |
| gptkbp:field |
gptkb:topology
homotopy theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Eilenberg–Mac Lane space
|
| gptkbp:introducedIn |
1945
|
| gptkbp:namedAfter |
gptkb:Saunders_Mac_Lane
gptkb:Samuel_Eilenberg |
| gptkbp:property |
π_k(K(G, n)) = 0 for k ≠ n
π_n(K(G, n)) ≅ G |
| gptkbp:usedIn |
gptkb:Postnikov_systems
gptkb:cohomology_theory gptkb:model_category_theory homotopy theory classifying spaces spectral sequences |
| gptkbp:bfsParent |
gptkb:Saunders_Mac_Lane
|
| gptkbp:bfsLayer |
5
|