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On characteristic classes and continuous cohomology. (English) Zbl 0609.57011

Supersymmetry and its applications: superstrings, anomalies and supergravity, Proc. Workshop, Cambridge/Engl. 1985, 29-40 (1986).
[For the entire collection see Zbl 0583.00021.]
In this paper the author reviews some facts from the theory of the characteristic classes and continuous cohomoloy. Namely, he shows how the continuous cohomology of a group measures the global informations needed to bring the infinitesimal computations (concerning the characteristic classes) into line with the global ones. The author considers only the finite dimensional case and gives an interesting example from the infinite dimensional case.
Reviewer: V.Oproiu

MSC:

57R20 Characteristic classes and numbers in differential topology
57T10 Homology and cohomology of Lie groups
58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)
57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology
55R40 Homology of classifying spaces and characteristic classes in algebraic topology
55N35 Other homology theories in algebraic topology
22E41 Continuous cohomology of Lie groups

Citations:

Zbl 0583.00021