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Kuperberg and Turaev-Viro Invariants in Unimodular Categories

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arxiv 1809.07991 v2 pith:GHM4CEBB submitted 2018-09-21 math.QA math.GT

Francesco Costantino , Nathan Geer , Bertrand Patureau-Mirand , Vladimir Turaev This is my paper · ORCID
classification math.QAmath.GT
keywords invariantscategorykuperbergturaev-virowhenalgebraboundarycalculus
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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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  1. Non-semisimple open-closed 3d TFT

    math.QA 2026-08 accept novelty 7.0 of 10

    A spherical finite tensor category with a modified trace gives a finite-dimensional open-closed 3d TFT via a new handlebody invariant and the universal construction.

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