Work

The Evaluation of Graphs on Surfaces for State-Sum Models with Defects

Year: 2024

Type: article

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.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2024.102

Authors: Universit&, Julian Farnsteiner, #228, t Hamburg, Germany, Christoph Schweigert, Universität Hamburg, Germany

Institution: Universität Hamburg

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Deutsche Forschungsgemeinschaft

Awards: G432818845, EXC 2121: Quantum Universe, G7488288221