Spectral sequence

In homological algebra, especially applied to algebraic topology or group cohomology, a spectral sequence is a sequence of differential modules (En,dn) such that

Examples

Some notable spectral sequences are:

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

• Leray-Serre spectral sequence of a fibration
• Hochschild-Serre spectral sequence in group cohomology
• Adams spectral sequence in stable homotopy theory
• Atiyah-Hirzebruch spectral sequence of an extraordinary cohomology theory
• Adams-Novikov spectral sequence for an extraordinary cohomology theory
• Grothendieck spectral sequence for composing derived functors
• Chromatic spectral sequence for the stable homotopy groups of spheres
• Eilenberg-Moore spectral sequence
• Bockstein spectral sequence