The Lyndon-Hochschild(-Serre) spectral sequence applies to group extensions in a manner analogous to the Serre-Leray spectral sequence applied to a fibration.


Does anyone know of a good description (or reference) of the transgression maps in the Lyndon-Hochschild spectral sequence? MacLane describes them in terms of an additive relation, but I don't find this helpful in computing them.


More generally, I don't know how to calculate the differentials in this spectral sequence. In the Serre spectral sequence, I can see how an exact couple arises and the differentials are straightforward to see if not easy to calculate. But the LHSS arises from a double complex and I'm not sure how to get an exact couple from this.



Differentials in the Lyndon-Hochschild spectral sequence
If you only need the first couple of transgressions, there is a nice description of them in the paper


[MR0641328 (83a:18021)
Huebschmann, Johannes
Automorphisms of group extensions and differentials in the Lyndon\mhy Hochschild\mhy Serre spectral sequence.
J. Algebra 72 (1981), no. 2, 296--334.](https://core.ac.uk/download/pdf/82585136.pdf)


For concrete calculations, this description is sometimes easier than the abstract nonsense description from the double complex.


