2000/08/11 by Marcos Marino, Marino, Marcos · 1 citation
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th #math.DG
paper · pdf · doi:10.48550/arxiv.hep-th/0008100
10 pages, LaTeX. Talk given at the 3rd ECM, Barcelona, July 2000; references added
arxiv created 2000/09/05 · arxiv updated 2009/11/30
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.