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arxiv: 1006.3501 · v5 · pith:QAYVNOGKnew · submitted 2010-06-17 · 🧮 math.GT · math.QA

On two approaches to 3-dimensional TQFTs

Vladimir Turaev , Alexis Virelizier This is my paper
classification 🧮 math.GT math.QA
keywords derivedinvariantmanifoldsapproachescategorycenterdimensionaldrinfeld-joyal-street
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Let C be a spherical fusion category. We prove that the Turaev-Viro-Barrett-Westbury state sum invariant of 3-manifolds derived from C is equal to the Reshetikhin-Turaev surgery invariant of 3-manifolds derived from Z(C), where Z(C) is the Drinfeld-Joyal-Street center of C.

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  1. A geometrical description of untwisted 3d Dijkgraaf-Witten TQFT with defects

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    A geometric construction of untwisted 3d Dijkgraaf-Witten TQFT with defects via gauge groupoid representations and fibrant spans of groupoids.