The Evaluation of Graphs on Surfaces for State-Sum Models with Defects
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, relevant to the Turaev-Viro construction with general defect configurations involvin...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212790 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Evaluation of Graphs on Surfaces for State-Sum Models with Defects. Julian Farnsteiner and Christoph Schweigert. SIGMA 20 (2024), 102, 51 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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, relevant to 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.
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| ISSN: | 1815-0659 |