Poincaré conjecture for dimensions five and higher
GPTKB entity
Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:concerns |
gptkb:homotopy_spheres
gptkb:topology manifolds |
| gptkbp:dimensions |
n ≥ 5
|
| gptkbp:field |
geometric topology
|
| https://www.w3.org/2000/01/rdf-schema#label |
Poincaré conjecture for dimensions five and higher
|
| gptkbp:influenced |
surgery theory
high-dimensional manifold theory |
| gptkbp:provenBy |
gptkb:Stephen_Smale
|
| gptkbp:relatedTo |
gptkb:Poincaré_conjecture
|
| gptkbp:state |
Every closed, simply connected n-manifold (n ≥ 5) is homeomorphic to the n-sphere
|
| gptkbp:status |
proven
|
| gptkbp:yearProved |
1961
|
| gptkbp:bfsParent |
gptkb:Smale's_theorem
|
| gptkbp:bfsLayer |
7
|