Cohomologie des groupes et des espaces de transformation. (Group cohomology and transformation spaces) (Q1096920)

The concept of a locally trivial extension of a transformation space (G,X) by a G-module A in a suitable category of topological spaces with superstructure (discrete, differential, algebraic,...) is introduced. This extends the notion of topologically locally trivial group extensions. Then, using group and equivariant Čech cohomology, a general cohomology theory for these extensions is developed. This can be used, for instance, to study their functorial or their reduction properties. This theory is applied, in another paper [ibid. 112, No.2, 349-369 (1988; see the following review Zbl 0634.55005)], to obtain cohomological descriptions of the varieties of pure spinors and of the spin groups.