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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.
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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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