Invertible Two Dimensional Topological Quantum Field Theories

Specialeforsvar ved Adrien Vakili

Titel: Invertible Two Dimensional Topologival Quatum Field Therories

Abstract: The TQFTs are the symmetric monoidal functors to some fixed target. When a TQFT factors through the cobordism groupoid, it is said to be invertible. In dimension two, Tillmann has shown that the cobordism groupoid is equivalent to an infinite cyclic group. As later remarked by Juer and Tillmann, a generator is given by the sphere. We provide a simplified version of Tillmann’s proof, which makes this latter fact evident. As an application, we exhibit a symmetric monoidal equivalence between the category of invertible TQFTs and the group of automorphisms of the target’s unit object. This generalizes a result of Juer and Tillmann.

Vejleder: Anssi Lahtinen
Censor: Iver Mølgaard Ottosen, AAU