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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