Thesis Information
Title: Dijkgraaf-Witten Theory For Surfaces
Program: Master of Arts in Mathematics
Advisor: Dr. Uwe Kaiser, Mathematics
Committee Members: Dr. Jens Harlander, Mathematics and Dr. Zach Teitler, Mathematics
Abstract
In this paper I talk about Dijkgraaf-Witten theory as it applies to surfaces. In the first section I give the necessary ingredients of a topological quantum field theory, including category theory, fiber bundles, and covering spaces, as well as providing physical motivation from the background of quantum field theory. The second section of this thesis contains a description of 2-dimensional TQFTs and their connection to Frobenius algebras. The construction of a particular class of TQFTs, Dijkgraaf- Witten theory, is contained in the third section, and the final section consists of interesting examples and further motivation for research in this direction.
