Topological Quantum Field Theory and Four-Manifolds
Marcos Mariño · Birkhäuser Basel eBooks · 2001
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 connections to three-manifold topology and to intersection theory on the moduli space of flat connections on Riemann surfaces; (c) four-dimensional theories with critical behaviour, which give some remarkable constraints on Seiberg-Witten invariants and new results on the geography of four-manifolds. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.