URegina Topology Seminar: Manak Singh

The Cobordism Hypothesis, as proposed by Baez and Dolan in 1995, provides a classification of n-extended Topological Quantum Field Theories (TQFTs). A n-extended TQFT is a symmetric monoidal n-functor from the n-category of cobordisms to an arbitrary symmetric monoidal n-category C. The hypothesis asserts that n-extended TQFTs correspond to fully dualizable objects in C. In 2008, Lurie outlined a proof for a more general statement, which implies the Baez & Dolan version as a consequence.

In Martin's talk we encountered the motivation for defining 2-extended TQFTs. I extend on this and show why it is natural to contemplate n-extended TQFTs. I discuss Lurie's (∞,n)-categorical version of the hypothesis and talk about what it means for an object to be fully dualizable in an (∞,n)-category.