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Topological Field Theory and Modular Tensor Categories

Banff International Research Station for Mathematical Innovation and Discovery

Abstract: Topological quantum field theories are invariants of manifolds which can be computed via cutting and gluing. This can be rephrased as a symmetric monoidal functor from a bordism category to the category . This connection can be exploited in both directions: using algebra to construct topological invariants, or using topology to prove algebraic theorems. An important generalization of the notion of an extended topological field theory, where one now allows further cutting along lower dimensional submanifolds. This can be again rephrased in terms of a functor from a symmetric monoidal n-category to a more algebraic n-category. Modular tensor categories appear very naturally when studying 321 extended field theories. The connection between MTC and TQFTS is originally due to Reshetikhin--Turaev, and I will take an approach inspired by more recent work of Bartlett--Douglas--Schommer-Pries--Vicary. I will begin with some simpler examples in lower dimensions.

Mathematics; Category theory; homological algebra; Quantum theory; Algebraic structures

video/mp4

Author affiliation: Indiana University

2017-02-16

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60602

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/