Transgression map
In algebraic topology, a transgression map is a way to transfer cohomology classes.
It occurs, for example in the inflation-restriction exact sequence in group cohomology, and in integration in fibers. It also naturally arises in many spectral sequences; see spectral sequence#Edge maps and transgressions.The transgression map appears in the inflation-restriction exact sequence, an exact sequence occurring in group cohomology. 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 AN = . Then the inflation-restriction exact sequence is:
The transgression map is the map H 1G/N → H 2
Transgression is defined for general n
only if HiG/N = 0 for i ≤ n-1.
