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Cohomology of the Yang-Mills gauge orbit space and dimensional reduction. (English) Zbl 0596.55003

This paper discusses the cohomology of the ”orbit space” \({\mathcal A}/{\mathcal G}_ 0\) for Yang-Mills theory. Here \({\mathcal A}\) is the space of connections on a principal SU(N) bundle P over a manifold V and \({\mathcal G}_ 0\) is the group of automorphisms of P which fix a base point. The cases when V is a sphere, or product of spheres are considered. As M. F. Atiyah and R. Bott showed [Philos. Trans. R. Soc. Lond., A 308, 523-615 (1982; Zbl 0509.14014)] the cohomology of \({\mathcal A}/{\mathcal G}_ 0\) can be described with standard methods of homotopy theory. On the other hand differential geometric methods can be used to give generators as explicit differential forms. The paper develops this from the point of view of differential geometry, tying up to the physics literature. The relations with modified Yang-Mills theories in \(2+1\) and \(3+1\) dimensions are discussed.
Reviewer: S.K.Donaldson

MSC:

55N99 Homology and cohomology theories in algebraic topology
55P99 Homotopy theory
81T08 Constructive quantum field theory
58D15 Manifolds of mappings

Citations:

Zbl 0509.14014
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References:

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