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Kuperberg and
Turaev–Viro invariants in unimodular categories
Francesco Costantino, Nathan Geer, Bertrand Patureau-Mirand and Vladimir Turaev |
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Vol. 306 (2020), No. 2, 421–450
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Abstract |
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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 semisimple and spherical. |
Keywords
quantum invariants, 3-manifold invariants, Heegaard
splitting, modified trace, pivotal category, Kuperberg
invariants
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Mathematical Subject Classification 2010
Primary: 18D10, 57M27
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Milestones
Received: 24 July 2019
Accepted: 7 January 2020
Published: 13 July 2020
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Authors |
| Francesco Costantino | |
| Institut de Mathématiques de
Toulouse III - Paul Sabotier Toulouse France |
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| Nathan Geer | |
| Department of Mathematics and
Statistics Utah State University Logan, UT United States |
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| Bertrand Patureau-Mirand | |
| UMR 6205, LMBA Université de Bretagne-Sud Campus Tohannic Vannes France |
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| Vladimir Turaev | |
| Department of Mathematics Indiana University Bloomington, IN United States |
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