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

Related Topics:
Homological algebra - Algebraic topology - Group cohomology - Differential module

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:En+1 = H(En) = ker dn / im dn

Related Topics:
Ker - Im

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is the homology of En.

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There are several ways in practice that such a 'linked' sequence can arise in homological algebra. Historically (since about 1950) spectral sequence arguments have been an important research tool, particularly in homotopy theory; even though, as explained by one of the leading experts, such a discussion may become 'too messy to publish in that form'. That is, they are intricate, certainly as compared to exact sequence arguments that are in effect a simple special case.

Related Topics:
Homotopy theory - Exact sequence

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