Serre spectral sequence
SPECTRAL SEQUENCE RELATING THE SINGULAR COHOMOLOGY OF THE TOTAL SPACE OF A SERRE FIBRATION IN TERMS OF THE COHOMOLOGIES OF THE BASE SPACE AND THE FIBER
Leray-Serre spectral sequence; Leray–Serre spectral sequence; Spectral sequence for the covering
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.