Serre Spectral Sequence

In mathematics, the Serre spectral sequence (sometimes Leray-Serre spectral sequence to acknowledge earlier work of Jean Leray in the Leray spectral sequence) is an important tool in algebraic topology. It expresses, in the language of homological algebra the singular (co)homology of the total space X of a (Serre) fibration in terms of the (co)homology of the base space B and the fiber F. The result is due to Jean-Pierre Serre in his doctoral dissertation.

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Homotopy Groups Of Spheres - Computational Methods
... for computing homotopy groups of spheres are based on spectral sequences (Ravenel 2003) ... suitable fibrations and taking the associated long exact sequences of homotopy groups spectral sequences are a systematic way of organizing the complicated information ... The method of killing homotopy groups", due to Cartan and Serre (1952a, 1952b) involves repeatedly using the Hurewicz theorem to compute the first non-trivial ...

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