Lie groups and Chern-Simons Theory

TL;DR

This paper provides an introduction to Lie groups and Chern-Simons theory, exploring their mathematical foundations and significance in topology, knot theory, and low-dimensional topology, aimed at graduate students.

Contribution

It offers a comprehensive lecture note resource connecting Lie groups with Chern-Simons theory, highlighting their role in modern mathematical physics and topology.

Findings

Introduces the mathematical framework of Chern-Simons theory.

Explores the role of Lie groups in topological invariants.

Provides educational material for graduate students.

Abstract

Witten introduced classical Chern-Simons theory to topology in 1989, when he defined an invariant for knots in 3-manifolds by an integral over a certain infinite-dimensional space, which up to today have not been entirely understood. However, they motivated lots of interesting questions and results in knot theory and low-dimensional topology, as well as the development of entirely new fields. These are lecture notes for a course in Lie groups and Chern-Simons Theory aimed at graduate students.