Abstract
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 will be applied, in another paper, to obtain cohomological descriptions of the varieties of pure spinors and of the spin groups.
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