Poincaré conjecture (higher dimensions)
GPTKB entity
Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:concerns |
homotopy sphere
n-manifold |
| gptkbp:dimensions |
n > 3
|
| gptkbp:field |
gptkb:topology
geometric topology |
| https://www.w3.org/2000/01/rdf-schema#label |
Poincaré conjecture (higher dimensions)
|
| gptkbp:provenBy |
gptkb:Michael_Freedman
gptkb:Stephen_Smale n = 4 n > 3 n ≥ 5 |
| gptkbp:relatedTo |
gptkb:Poincaré_conjecture
|
| gptkbp:seeAlso |
gptkb:h-cobordism_theorem
gptkb:Generalized_Poincaré_conjecture gptkb:Poincaré_conjecture_(3-dimensional) gptkb:exotic_spheres |
| gptkbp:sentence |
Every closed, simply connected n-manifold is homeomorphic to the n-sphere for n > 3.
|
| gptkbp:status |
proven for n = 4
proven for n ≥ 5 |
| gptkbp:yearProved |
1961
1982 |
| gptkbp:bfsParent |
gptkb:Stephen_Smale
|
| gptkbp:bfsLayer |
5
|