Notes on Topological Field Theory

Introduction The notes give a survey of the basics of the following topological field theories: • The Chern-Simons gauge theory on 3-manifolds, its renormalization, geometric quantization, computation of partition functions by surgery, and relation with Jones Polynomials • Twisted N = 2 supersymmetric Yang-Mills theory on 4-manifolds, its reduction to N = 1 theory with a mass gap, and computation of Donaldson’s polynomials • Topological sigma model, A-model open string interpretation of Chern-Simons gauge theory, and the duality between topological closed string and Chern-Simons theory.