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Topological gauge theories and group cohomology. (English) Zbl 0703.58011
The paper starts with a review of the singular homology and cohomology theory of topological spaces and the construction of topological actions. Considering that the three dimensional topological (Chern-Simons) theories are classified by classes in \(H^4(BG,Z)\) and the two dimensional Wess-Zumino actions are classified by classes of \(H^3(G,Z)\) the relation between these two theories is established through a natural map \(H^4(BG,Z)\to H^3(G,Z)\). This construction is extended to manifolds with spin structure. Finally, topological gauge theories with finite groups are discussed and related to two dimensional orbifold models.
Reviewer: V.Silveira

MSC:
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
57R20 Characteristic classes and numbers in differential topology
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
81T13 Yang-Mills and other gauge theories in quantum field theory
81T70 Quantization in field theory; cohomological methods
20J06 Cohomology of groups
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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