The Leray-Hirsch Theorem is a basic result on the algebraic topology of fiber bundles, giving conditions under which the cohomology of the total space of a fiber bundle can be computed from the cohomology of the base space together with the cohomology of the fiber. Named for Jean Leray and Guy Hirsch, who independently proved it in the late 1940s, it can be viewed as a mild generalization of the Kunneth Theorem for product spaces, and is itself a special case of the more general Leray spectral sequence.
Facts
StatementFor a fibre bundle E over B with fibre F such that each H^p(F;Q) is finite-dimensional and the inclusion of F into E induces a surjection in rational cohomology, choosing a section s of that surjection makes the map H*(F) tensor H*(B) to H*(E), sending alpha tensor beta to s(alpha) cup pi*(beta), an isomorphism of H*(B)-modules. 1 Classification
Statement FormCharacterization Theorem 1 Connections
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. Leray-Hirsch theorem (Wikipedia)
Statement in coordinatesQuote, Statement in coordinates
the map given below is then an isomorphism of
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