Topological quantum field theory and four-manifolds

Details Topological quantum field theory and four-manifolds Topological quantum field theory and four-manifolds

2000-08-11

arxiv.org/abs/hep-th/0008100v2

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, LaTeX. Talk given at the 3rd ECM, Barcelona, July 2000; references added

Scientific paper

I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit results for the Donaldson invariants of non-simply connected manifolds, and for generalizations of these invariants to the gauge group SU(N); (b) compactifications to lower dimensions, and relations with three-manifold topology and with intersection theory on the moduli space of flat connections on Riemann surfaces; (c) four-dimensional theories with critical behavior, which give some remarkable constraints on Seiberg-Witten invariants and new results on the geography of four-manifolds.

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