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A vital part of Jacob Lurie's classification of fully extended topological field theories [1], very roughly, says that any representation of the n-Cobordism category $Z: {\rm Cob}_{{n}} \to C$ depends …

In the physics literature the Holographic Principle relates theories in the bulk and the theories in the asymptotic boundary. While the bulk theory is the 3D Chern-Simons theory, the corresponding bou …

Non-extendable 2D TQFTs correspond to finite dimensional Frobenius algebras [1]. How about 3D TQFTs? While the answer is clear for the extended ones (e.g. (3,2,1) TQFTs almost correspond to modular te …

I am interested in state sum models and their relations with some other of TQFTs, especially the fully extended TQFTs and the Dijkgraaf-Witten TQFTs (generalized, in the sense that finite-group-bundle …

Question Let $H$ be a finite dimensional complex Hopf algebra and $D(H)$ its quantum double. Can we classify the simple objects in $\operatorname{Rep}D(H)$ if the representations of $H$ are well-unde …

I haven't seen this question in standard textbooks, so I decide to give it a try here. It might relate to deeper structures of certain TQFTs, but I'm not sure. Let $G$ be a finite group. Its finite-di …

This is a jargon-like question. The fact that this is posted here rather in a physics forum indicates two things I know too little physics. An explanation with more mathematics flavors will be appr …

I am learning TQFT from compact Lie groups by Freed, Hopkins, Lurie, and Teleman: https://arxiv.org/abs/0905.0731 , and got stuck very hard even in the first section ($n = 1$), which was "trivial but …