Higher bundle gerbes and cohomology classes in gauge theories. (English) Zbl 0884.55004
The paper deals with geometrical realization of integral cohomology classes of certain manifolds. These manifolds arise from gauge theories. The tool introduced the achieve this goal is the notion of higher bundle gerbe. After reviewing the results known for bundle 1-gerbes (and proving that the product is associative), the authors introduce the notion of bundle 2-gerbe (for the higher cases the definition is just sketched) and they prove that the product is associative. In the last part of the paper they use this tool to realize some cohomology classes arising naturally in gauge theory: Faddeev-Mickelsson cocycle, the degree 4 de Rham cohomology of the space of connections modulo the gauge action.
Reviewer: M.Saralegi-Aranguren (Lenz)
MSC:
| 55N30 | Sheaf cohomology in algebraic topology |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 46M20 | Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) |
| 57R95 | Realizing cycles by submanifolds |
Keywords:
geometrical realization; integral cohomology; manifolds; bundle gerbe; gauge theory; Faddeev-Mickelsson cocycleReferences:
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