# Leray-Hirsch theorem for cohomology

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*You might be looking for:* Leray-Hirsch theorem for K-theory

## Statement

Let be a fiber bundle with fiber space , and be a commutative unital ring, such that the following hold:

- is a finitely generated free -module for every
- There exist classes whose restrictions form a basis for in each fiber , via the inclusion of the fiber in (the choice of these classes needs to be made independent of the fiber)

Then the map:

given by:

is an isomorphism.