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arXiv · 1706.01845

Abelian Turaev-Virelizier theorem and $U(1)$ BF surgery formulas

Ph. Mathieu·F. Thuillier
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Abstract

In this article we construct the Reshetikhin-Turaev invariant associated with the Drinfeld Center of the spherical category arising from the $U(1)$ BF theory on a closed $3$-manifold $M$. This invariant is shown to coincide with the Turaev-Viro invariant of $M$ thus providing an example of the Turaev-Virelizier theorem. Finally we exhibit some surgery formulas for the abelian Turaev-Viro invariant which are very similar to the surgery formulas of the abelian Reshetikhin-Turaev invariant obtained in the $U(1)$ Chern-Simons context.

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Ph. Mathieu, F. Thuillier. 2017-06-06. Abelian Turaev-Virelizier theorem and $U(1)$ BF surgery formulas. https://doi.org/10.1063/1.4986850

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