Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
n-sphere |
| gptkbp:borders |
none
|
| gptkbp:canBeEmbeddedIn |
R^5
|
| gptkbp:category |
gptkb:Riemannian_manifold
homogeneous space |
| gptkbp:defines |
set of points in 5-dimensional Euclidean space at unit distance from a fixed point
|
| gptkbp:dimensions |
4
|
| gptkbp:Euler_characteristic |
2
|
| gptkbp:fundamentalGroup |
trivial
|
| gptkbp:generalizes |
gptkb:butter
gptkb:3-sphere 2-sphere |
| gptkbp:homology_group_H_0 |
Z
|
| gptkbp:homology_group_H_1 |
0
|
| gptkbp:homology_group_H_2 |
0
|
| gptkbp:homology_group_H_3 |
0
|
| gptkbp:homology_group_H_4 |
Z
|
| https://www.w3.org/2000/01/rdf-schema#label |
4-sphere
|
| gptkbp:relatedTo |
gptkb:Poincaré_conjecture
gptkb:exotic_spheres |
| gptkbp:surface_area_formula |
(π^2)(2)^4/2! = 8π^2 for unit radius
|
| gptkbp:symbol |
S^4
|
| gptkbp:topology |
simply connected
compact manifold |
| gptkbp:used_in |
gptkb:geometry
gptkb:topology physics |
| gptkbp:volume_formula |
(8/3)π^2 for unit radius
|
| gptkbp:bfsParent |
gptkb:S^3-bundles_over_S^4
gptkb:quaternionic_Hopf_fibration |
| gptkbp:bfsLayer |
6
|