Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
orientable closed manifolds
|
| gptkbp:category |
gptkb:topology
|
| gptkbp:describes |
relationship between homology and cohomology
|
| gptkbp:field |
gptkb:topology
|
| gptkbp:generalizes |
gptkb:Lefschetz_duality
gptkb:Alexander_duality |
| https://www.w3.org/2000/01/rdf-schema#label |
Poincaré duality
|
| gptkbp:namedAfter |
gptkb:Henri_Poincaré
|
| gptkbp:relatedTo |
gptkb:de_Rham_cohomology
intersection theory cup product fundamental class |
| gptkbp:requires |
manifold to be closed
manifold to be orientable |
| gptkbp:state |
k-th cohomology group is isomorphic to (n−k)-th homology group
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
differential geometry manifold theory |
| gptkbp:yearProposed |
1895
|
| gptkbp:bfsParent |
gptkb:Henri_Poincaré
gptkb:Serre_duality |
| gptkbp:bfsLayer |
5
|