Statements (34)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
smooth manifolds
PL-manifolds topological manifolds |
| gptkbp:class |
classified in dimensions greater than 4
not all homotopy spheres are diffeomorphic to standard spheres |
| gptkbp:definedIn |
manifolds homotopy equivalent to a standard sphere
|
| gptkbp:dimensions |
n-dimensional
|
| gptkbp:field |
gptkb:topology
differential topology |
| gptkbp:groupStructure |
group under connected sum
|
| gptkbp:hasInvariant |
homotopy type
differentiable structure diffeomorphism type homeomorphism type |
| gptkbp:hasSpecialCase |
gptkb:exotic_spheres
|
| https://www.w3.org/2000/01/rdf-schema#label |
homotopy spheres
|
| gptkbp:importantFor |
Milnor discovered 7-dimensional exotic spheres
|
| gptkbp:notation |
Σ^n
|
| gptkbp:relatedTo |
gptkb:h-cobordism_theorem
gptkb:Poincaré_conjecture homeomorphism surgery theory diffeomorphism differentiable structures stable homotopy theory PL-manifolds smooth structures on spheres |
| gptkbp:standardExample |
n-sphere
|
| gptkbp:studiedBy |
gptkb:John_Milnor
1950s |
| gptkbp:bfsParent |
gptkb:Milnor–Kervaire_theorem
gptkb:exotic_spheres |
| gptkbp:bfsLayer |
5
|