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.
Inflation-restriction exact sequence
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 acts onThen the inflation-restriction exact sequence is:
The transgression map is the map.
Transgression is defined for general,
only if for.