Lecture Notes on Topological Field Theory
Jian Qiu

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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Black Holes and Theoretical Physics
