The Serre spectral sequence is a powerful tool in algebraic topology and homological algebra that provides a method for computing the homology (or cohomology) of a space that can be decomposed into simpler pieces, often using a fibration or a cellular decomposition. ### Overview The Serre spectral sequence arises particularly in the context of a fibration sequence, which is a type of map between topological spaces characterized by having certain lifting properties.
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For a fibration with suitable connectivity, the cohomological Serre spectral sequence haswith differential .