Kuperberg and Turaev-Viro Invariants in Unimodular Categories
Quantum Algebra
2020-07-15 v2 Geometric Topology
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.
Keywords
Cite
@article{arxiv.1809.07991,
title = {Kuperberg and Turaev-Viro Invariants in Unimodular Categories},
author = {Francesco Costantino and Nathan Geer and Bertrand Patureau-Mirand and Vladimir Turaev},
journal= {arXiv preprint arXiv:1809.07991},
year = {2020}
}
Comments
30 pages, 24 figures