English

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