Statements (50)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
smooth manifolds
PL-manifolds topological manifolds |
| gptkbp:class |
classified in high dimensions by Kervaire and Milnor
|
| gptkbp:definedIn |
manifolds homotopy equivalent to a standard sphere
|
| gptkbp:dimensions |
n-dimensional
|
| gptkbp:discoveredBy |
1956
|
| gptkbp:example |
gptkb:Milnor_sphere
|
| gptkbp:field |
gptkb:topology
differential topology |
| gptkbp:first_constructed_by |
gptkb:John_Milnor
|
| gptkbp:group_name |
homotopy sphere group Θ_n
|
| 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:notation |
Σ^n
|
| gptkbp:number_in_dimension_7 |
28
|
| gptkbp:property |
can be exotic in dimension 7
may not be diffeomorphic to standard sphere always homeomorphic to standard sphere in dimension 3 |
| gptkbp:relatedTo |
gptkb:h-cobordism_theorem
gptkb:Kervaire_invariant gptkb:exotic_7-sphere gptkb:Poincaré_conjecture gptkb:sphere_theorem gptkb:Borel_conjecture gptkb:smooth_Poincaré_conjecture surgery theory differentiable structures on spheres homotopy group of spheres stable homotopy theory exotic smooth structures Eells-Kuiper invariant PL Poincaré conjecture PL structures on S^n PL structures on spheres diffeomorphism group of spheres differentiable structures on S^n exotic 4-sphere (unknown existence) h-cobordism group homeomorphism group of spheres surgery obstruction |
| gptkbp:structure |
forms group under connected sum
|
| gptkbp:studiedBy |
gptkb:John_Milnor
|
| gptkbp:bfsParent |
gptkb:High-dimensional_Knot_Theory
|
| gptkbp:bfsLayer |
7
|