In mathematics, the inflation-restriction exact sequence is an exact sequence occurring in group cohomology and is a special case of the five-term exact sequence arising from the study of spectral sequences.
Specifically, let G be a group, N a normal subgroup, and A an abelian group which is equipped with an action of G, i.e., a homomorphism from G to the automorphism group of A.
The quotient group G/N acts on Then the inflation-restriction exact sequence is: In this sequence, there are maps The inflation and restriction are defined for general n: The transgression is defined for general n only if Hi(N, A)G/N = 0 for i ≤ n − 1.
[1] The sequence for general n may be deduced from the case n = 1 by dimension-shifting or from the Lyndon–Hochschild–Serre spectral sequence.
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