Statements (30)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
gptkb:Riemannian_manifold |
| gptkbp:can_be_defined_as |
unit sphere in 8-dimensional Euclidean space
set of points in R^8 at unit distance from the origin |
| gptkbp:category |
gptkb:geometry
gptkb:topology |
| gptkbp:dimensions |
7
|
| gptkbp:Euler_characteristic |
0
|
| gptkbp:fundamentalGroup |
trivial
|
| gptkbp:has_special_property |
parallelizable
|
| gptkbp:homotopy_group_π_7(S^7) |
Z
|
| https://www.w3.org/2000/01/rdf-schema#label |
7-sphere
|
| gptkbp:relatedTo |
gptkb:Bott_periodicity
gptkb:Hopf_fibration gptkb:exotic_spheres gptkb:octonions Lie group structure (not a group, but has a multiplication from octonions) |
| gptkbp:surface_area_formula |
(16π^3)/105
|
| gptkbp:symbol |
S^7
|
| gptkbp:type |
gptkb:topology
gptkb:Riemannian_manifold gptkb:hypersphere n-sphere compact manifold simply connected space |
| gptkbp:volume_formula |
π^4/3
|
| gptkbp:bfsParent |
gptkb:7-dimensional_sphere
gptkb:octonionic_Hopf_fibration gptkb:quaternionic_Hopf_fibration |
| gptkbp:bfsLayer |
6
|