Serre spectral sequence
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In mathematics, the Serre spectral sequence (sometimes Leray-Serre spectral sequence to acknowledge earlier work of Jean Leray) is a basic tool of algebraic topology. In a fibration with base space B and total space E, and with fiber F, it is a spectral sequence beginning with the terms
- E2pq = Hp(B, Hq(F)),
where the inner group on the right is the q-th integral cohomology group of F, and the outer group is the singular cohomology of B with coefficients in that group. Its abutment is formed by the groups
- Hn(E)
which are the cohomology groups of the total space. This result is due to Jean-Pierre Serre in his doctoral dissertation (Serre's thesis).