Classifying 3-dimensional TQFTs via generators and relations.

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• Chris Schommer-Pries, MPI Bonn
• Wednesday 21 May 2014, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

I will give an overview of joint work establishing a simple generators-and-relations presentation of the 3-dimensional oriented bordism bicategory, and also its “signature” central extension. The methods use a mixture of 2-dimensional category theory and 2-dimensional Morse theory (aka 2-Morse theory). This presentation gives a simple classification of representations of this bicategory in any target 2-category (aka TQF Ts with that target). When the target is linear categories, functors, and transformations we obtain the expected result that representations correspond in a 2-1 fashion to modular tensor categories, which must be anomaly-free in the oriented case. J/w with Bruce Bartlett, Chris Douglas, and Jamie Vicary.

This talk is part of the Differential Geometry and Topology Seminar series.

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