One feature of these fermionic based on Berezin integral theories is that they are quite straightforwardly generalized to any dimensions, not just 3 - which, by the way, provides you with a powerful and intriguing means of studying 3-manifolds using 4-manifolds, etc. These new theories are related to Lie groups without any obvious restrictions as for semisimplicity etc. The proof goes by an explicit generators and relations presentation of the 3d cobordism category in terms of surgeries and automorphisms of surfaces.
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- Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners.
Asked 9 years, 11 months ago. Active 1 year, 10 months ago. Viewed 2k times. Ilya Nikokoshev 8, 10 10 gold badges 60 60 silver badges bronze badges. Kevin Walker Kevin Walker 9, 2 2 gold badges 30 30 silver badges 77 77 bronze badges. Can someone remind me what the situation is here? The modularity condition cannot be formulated without assuming a braiding.
Papers on Topological Quantum Field Theory (TQFT)
Noah Snyder Noah Snyder 20k 2 2 gold badges 68 68 silver badges bronze badges. I would be happily surprised if someone had worked out a non-semisimple example which gave a functor on 3-dimensional bordisms and was well-behaved axiomatically. Lin Oct 13 '09 at What about the book "Non-semisimple topological quantum field theories for 3-manifolds with corners"?
The anomaly they use is "exotic" my word and corresponds to a central extension of the bordism 2-category, not by a group but by a monoid I think it was the natural numbers. K3 surface is an example of a non-semi-simple 3d TQFT.
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Igor Korepanov Igor Korepanov 76 1 1 silver badge 6 6 bronze badges. Now fermionic formulas are my attempt to go outside that framework think it looks natural in 21st century ; see also a 4d paper arxiv. Cheers, I. Is there any discussion anywhere how his results specialise to strong monoidal functors?
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Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners
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