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- W2782692232 abstract "A 3-dimensional topological quantum field theory (TQFT) is a symmetric monoidal functor from the category of 3-cobordisms to the category of vector spaces. Such TQFTs provide in particular numerical invariants of closed 3-manifolds and representations of the mapping class group of closed surfaces.In 1994, Turaev explains how to construct a TQFT from a modular category; the scalar invariant is then the Reshethikhin-Turaev invariant introduced in 1991. In this thesis, we describe a generalization of this construction starting from a ribbon category C with coend. We present a cobordism by a certain type of tangle (cobordism tangle) and we associate to such a tangle a morphism between tensor products of the coend as described by Lyubashenko in 1994. Extending the Kirby calculus to 3-cobordisms, we obtain in this way an invariant of cobordisms and a TQFT which takes values in the symmetric monoidal subcategory of transparent objects of C. If the category C is modular, this subcategory can be identified with the category of vector spaces, and we recover Turaev's TQFT. If the category C is modularizable, our TQFT is a lift of the Turaev TQFT for the modularization of C." @default.
- W2782692232 created "2018-01-26" @default.
- W2782692232 creator A5090548123 @default.
- W2782692232 date "2016-10-31" @default.
- W2782692232 modified "2023-09-23" @default.
- W2782692232 title "Internal Reshetikhin-Turaev Topological Quantum Field Theories" @default.
- W2782692232 hasPublicationYear "2016" @default.
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