The Eilenberg-Moore spectral sequence is a powerful tool in algebraic topology and homological algebra used to compute the homology or cohomology of a space from the data of a fibration. It arises in the context of studying fibrations and can be thought of as a way to relate the homological properties of a fibration's base space, total space, and fiber. This spectral sequence provides insight into the relationships between different cohomological invariants, making it invaluable for understanding complex topological spaces.
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