De Rham's Theorem, a result of differential geometry, states that the ring homomorphism from a manifold's de Rham cohomology to its singular cohomology, given by integrating differential forms over cycles, is an isomorphism. The Poincare Lemma already shows abstractly that de Rham cohomology is isomorphic as a group to sheaf cohomology with the constant real-number sheaf, and hence to singular cohomology, but de Rham's Theorem supplies a considerably more explicit isomorphism between the two, connecting analysis and topology more directly.
Facts
Partially Attested
Proof YearSource says de Rham set out in 1931 to give a rigorous proof; completion year is not stated. StatementThe ring homomorphism from the de Rham cohomology to the singular cohomology given by integration is an isomorphism. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Associated With
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. De Rham theorem (Wikipedia)
Lead paragraph, sentence 1Quote, Lead paragraph, sentence 1
the de Rham theorem says that the ring homomorphism from the de Rham cohomology to the singular cohomology given by integration is an isomorphism
2. Georges de Rham (MacTutor History of Mathematics)
BiographyQuote, Biography
But in 1931 de Rham set out to give a rigorous proof.
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