Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:topology
|
| gptkbp:abbreviation |
gptkb:K(G,_n)
|
| gptkbp:category |
gptkb:homotopy_category
|
| gptkbp:characterizedBy |
π_n(X) = G, π_k(X) = 0 for k ≠ n
|
| gptkbp:example |
circle S^1 is K(ℤ, 1)
infinite-dimensional complex projective space is K(ℤ, 2) |
| gptkbp:fundamentalGroup |
G (if n=1)
|
| gptkbp:hasApplication |
gptkb:Postnikov_tower
homological algebra classifying spaces spectral sequences |
| gptkbp:hasProperty |
gptkb:CW_complex
connected if n > 0 simply connected if n > 1 unique up to homotopy equivalence |
| gptkbp:homotopyGroup |
π_k = 0 for k ≠ n
π_n = G |
| gptkbp:introducedIn |
1950s
|
| gptkbp:namedAfter |
gptkb:Saunders_Mac_Lane
gptkb:Samuel_Eilenberg |
| gptkbp:parameter |
group G
integer n |
| gptkbp:usedFor |
classifying cohomology classes
representing cohomology functors |
| gptkbp:usedIn |
gptkb:topology
gptkb:cohomology_theory homotopy theory |
| gptkbp:bfsParent |
gptkb:Samuel_Eilenberg
gptkb:David_Eilenberg |
| gptkbp:bfsLayer |
6
|
| https://www.w3.org/2000/01/rdf-schema#label |
Eilenberg–MacLane space
|