de Rham theorem
E1533546
UNEXPLORED
The de Rham theorem is a fundamental result in differential geometry that identifies the de Rham cohomology of a smooth manifold with its singular cohomology with real coefficients, linking differential forms to topological invariants.
All labels observed (2)
| Label | Occurrences |
|---|---|
| de Rham theorem canonical | 3 |
| de Rham isomorphism | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T22329090 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: de Rham theorem Context triple: [de Rham cohomology, satisfies, de Rham theorem]
-
A.
de Rham cohomology
de Rham cohomology is a cohomology theory for smooth manifolds that uses differential forms to capture their global topological and geometric properties.
-
B.
Čech–de Rham complex
The Čech–de Rham complex is a double complex that combines Čech cochains with differential forms to compute de Rham cohomology via open covers.
-
C.
Mayer–Vietoris sequence in de Rham cohomology
The Mayer–Vietoris sequence in de Rham cohomology is a long exact sequence that computes the de Rham cohomology of a manifold by relating it to the cohomology of an open cover and their intersection.
-
D.
Chern–Weil theory
Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
-
E.
Poincaré duality
Poincaré duality is a fundamental theorem in algebraic topology that relates the homology and cohomology groups of an oriented closed manifold in complementary dimensions.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: de Rham theorem Target entity description: The de Rham theorem is a fundamental result in differential geometry that identifies the de Rham cohomology of a smooth manifold with its singular cohomology with real coefficients, linking differential forms to topological invariants.
-
A.
de Rham cohomology
de Rham cohomology is a cohomology theory for smooth manifolds that uses differential forms to capture their global topological and geometric properties.
-
B.
Čech–de Rham complex
The Čech–de Rham complex is a double complex that combines Čech cochains with differential forms to compute de Rham cohomology via open covers.
-
C.
Mayer–Vietoris sequence in de Rham cohomology
The Mayer–Vietoris sequence in de Rham cohomology is a long exact sequence that computes the de Rham cohomology of a manifold by relating it to the cohomology of an open cover and their intersection.
-
D.
Chern–Weil theory
Chern–Weil theory is a framework in differential geometry that constructs characteristic classes of vector bundles from curvature forms, linking topology and geometry through invariant polynomials.
-
E.
Poincaré duality
Poincaré duality is a fundamental theorem in algebraic topology that relates the homology and cohomology groups of an oriented closed manifold in complementary dimensions.
- F. None of above. chosen
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: de Rham theorem