Lecture Notes on Topological Field Theory

TL;DR

This paper provides an overview of topological Chern-Simons theory, covering both perturbative and non-perturbative aspects, including quantization, surgery, and applications to knot invariants.

Contribution

It offers a comprehensive lecture-based synthesis of key topics in topological field theory, emphasizing recent developments in quantization and invariants.

Findings

Quantization methods for Chern-Simons theory

Use of surgery techniques for computations

Connections to knot invariants and topological invariants

Abstract

These notes are based on the lecture the author gave at the workshop 'Geometry of Strings and Fields' held at Nordita, Stockholm. In these notes, I shall cover some topics in both the perturbative and non-perturbative aspects of the topological Chern-Simons theory. The non-perturbative part will mostly be about the quantization of Chern-Simons theory and the use of surgery for computation, while the non-perturbative part will include brief discussions about framings, eta invariants, APS-index theorem, torsions and finite type knot invariants.