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In Bott and Tu's Differential forms in algebraic topology there is a proof of Leray-Hirsch for the De Rham cohomology. The theorem is this: Theorem (Leray-Hirsch): Let $E$ be a fiber bundle over $M$...

On Bott's paper "Homogeneous vector bundles" there is the following statement of Leray spectral sequence: Let $X$ and $Y$ be paracompact and locally compact spaces and $f : Y \to X$ be a proper map....

Let $E \to B$ be a topological fiber bundle. We know that the Serre spectral sequence allows you to compute the cohomology of $E$ with constant coefficient in terms of the cohomology of $F$ and the ...