Kuperberg and Turaev-Viro Invariants in Unimodular Categories
arXiv:1809.07991 · doi:10.2140/pjm.2020.306.421
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.
30 pages, 24 figures