Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:butter
gptkb:mathematical_concept |
| gptkbp:alsoKnownAs |
gptkb:7-sphere
|
| gptkbp:category |
gptkb:topology
differential geometry higher-dimensional geometry |
| gptkbp:definedIn |
set of points in 8-dimensional Euclidean space at unit distance from a fixed point
|
| gptkbp:dimensions |
7
|
| gptkbp:embeddingDimension |
8
|
| gptkbp:groupStructure |
can be given a Lie group structure as the unit octonions
|
| 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
|
| gptkbp:HopfFibration |
S^7 → S^4 with fiber S^3
|
| https://www.w3.org/2000/01/rdf-schema#label |
7-dimensional sphere
|
| gptkbp:parallelizable |
true
|
| gptkbp:parallelizableSpheres |
S^1, S^3, S^7
|
| gptkbp:relatedTo |
gptkb:Hopf_fibration
gptkb:octonions |
| gptkbp:surfaceAreaFormula |
(16π^3)/105
|
| gptkbp:symbol |
S^7
|
| gptkbp:topologicalType |
simply connected
compact manifold |
| gptkbp:volume |
π^4/3!
|
| gptkbp:bfsParent |
gptkb:exotic_spheres
|
| gptkbp:bfsLayer |
5
|