The Leray–Serre spectral sequence is a powerful tool in algebraic topology that helps compute the cohomology of a space by relating it to the cohomology of its subspaces and a fibration. It is particularly useful in cases where you have a fibration and you want to derive information about the total space from the base and fiber spaces. This sequence plays a critical role in the cohomology of groups, especially when analyzing their topological properties through fiber bundles.
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