The Evaluation of Graphs on Surfaces for State-Sum Models with Defects
Quantum Algebra
2024-11-19 v2 Mathematical Physics
Category Theory
math.MP
Abstract
The evaluation of graphs on 2-spheres is a central ingredient of the Turaev-Viro construction of three-dimensional topological field theories. In this article, we introduce a class of graphs, called extruded graphs, that is relevant for the Turaev-Viro construction with general defect configurations involving defects of various dimensions. We define the evaluation of extruded graphs and show that it is invariant under a set of moves. This ensures the computability and uniqueness of our evaluation.
Keywords
Cite
@article{arxiv.2312.01946,
title = {The Evaluation of Graphs on Surfaces for State-Sum Models with Defects},
author = {Julian Farnsteiner and Christoph Schweigert},
journal= {arXiv preprint arXiv:2312.01946},
year = {2024}
}