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arXiv · 1809.07991

Kuperberg and Turaev-Viro Invariants in Unimodular Categories

Francesco Costantino·Nathan Geer·Bertrand Patureau-Mirand·Vladimir Turaev
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Abstract

We give a categorical setting in which Penrose graphical calculus naturally extends to graphs drawn on the boundary of a handlebody. We use it to introduce invariants of 3-manifolds presented by Heegaard splittings. We recover Kuperberg invariants when the category comes from an involutory Hopf algebra and Turaev-Viro invariants when the category is semi-simple and spherical.

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Francesco Costantino, Nathan Geer, Bertrand Patureau-Mirand, Vladimir Turaev. 2018-09-21. Kuperberg and Turaev-Viro Invariants in Unimodular Categories. https://doi.org/10.2140/pjm.2020.306.421

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