Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:butter
gptkb:mathematical_concept exotic spheres (in 7 dimensions, there exist exotic spheres) |
| gptkbp:canBeEmbeddedIn |
R^8
|
| gptkbp:definedIn |
set of points in 8-dimensional Euclidean space at unit distance from the origin
|
| gptkbp:dimensions |
7
|
| gptkbp:groupStructure |
can be given a non-associative multiplication (related to octonions)
|
| gptkbp:hasParallelizableTangentBundle |
true
|
| gptkbp:homologyGroup |
H_0(S^7) = Z
H_7(S^7) = Z H_k(S^7) = 0 for 0 < k < 7 |
| gptkbp:homotopyGroup |
π_7(S^7) = Z
|
| https://www.w3.org/2000/01/rdf-schema#label |
standard 7-sphere
|
| gptkbp:relatedTo |
gptkb:octonions
|
| gptkbp:symbol |
S^7
|
| gptkbp:topologicalType |
simply connected
compact manifold |
| gptkbp:universalCover |
S^7/Γ for finite subgroups Γ
|
| gptkbp:bfsParent |
gptkb:exotic_7-sphere
|
| gptkbp:bfsLayer |
6
|