Statements (19)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:Closed_orientable_manifolds
|
| gptkbp:category |
gptkb:Mathematics
gptkb:Topology |
| gptkbp:field |
gptkb:Algebraic_topology
|
| gptkbp:firstPublished |
1895
|
| 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:Cohomology
Homology |
| gptkbp:state |
The kth homology group is isomorphic to the (n−k)th cohomology group for an n-dimensional closed orientable manifold
|
| gptkbp:usedIn |
gptkb:Morse_theory
gptkb:De_Rham_cohomology gptkb:Intersection_theory Characteristic classes |
| gptkbp:bfsParent |
gptkb:Singular_Homology_Theory
|
| gptkbp:bfsLayer |
7
|