Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:topology
|
| gptkbp:alsoKnownAs |
gptkb:Eilenberg–MacLane_space
|
| gptkbp:built |
can be constructed as a CW complex
|
| gptkbp:category |
homotopy type
|
| gptkbp:example |
K(Z, 1) is the circle S^1
K(Z, 2) is the infinite complex projective space CP^∞ K(Z/2Z, 1) is the infinite real projective space RP^∞ |
| https://www.w3.org/2000/01/rdf-schema#label |
K(G, n)
|
| gptkbp:namedAfter |
gptkb:Saunders_Mac_Lane
gptkb:Samuel_Eilenberg |
| gptkbp:parameter |
G
n |
| gptkbp:property |
unique up to homotopy equivalence
all other homotopy groups are trivial classifying space for principal G-bundles when n=1 exists for any abelian group G and integer n ≥ 1 homotopy group π_n is isomorphic to G represents cohomology functor H^n(-, G) |
| gptkbp:usedIn |
gptkb:topology
gptkb:cohomology_theory homotopy theory |
| gptkbp:bfsParent |
gptkb:Eilenberg–Mac_Lane_space
|
| gptkbp:bfsLayer |
6
|