These third–year lecture notes are designed for a 1–semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second–year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism.
In these lectures we present a general introduction to topological quantum field theories. These theories are discussed in the framework of the Mathai-Quillen formalism and in the context of twisted N = 2 supersymmetric theories. We discuss in detail the recent developments in Do
These notes are meant to provide an introduction to topological quantum field theory for mathematicians. Topics include applications of Chern-Simons theory to the study of knots and Atiyah’s definition of a topological quantum field theory. We also include a self-contained introd
The goal of this course is to define invariants of 3-manifolds and knots and representations of the mapping class group, using quantum field theory. We will follow Kohno, Conformal Field Theory and Topology, supplementing it with additional material to make it more accessible. Th
We present a summary of the progress made in the last few years on topological quantum field theory in four dimensions. In particular, we describe the role played by duality in the developments which led to the Seiberg-Witten invariants and their relation to the Donaldson invaria
Topological quantum field theories (TQFT) provide powerful tools to probe topology of manifolds, specifically in low dimensions[1, 2, 3, 4, 5]. This is achieved by incorporating very large gauge symmetries in the theory which lead to gauge invariant sectors with only topological