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...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2024 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212790 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Evaluation of Graphs on Surfaces for State-Sum Models with Defects. Julian Farnsteiner and Christoph Schweigert. SIGMA 20 (2024), 102, 51 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862680760957272064 |
|---|---|
| author | Farnsteiner, Julian Schweigert, Christoph |
| author_facet | Farnsteiner, Julian Schweigert, Christoph |
| citation_txt | The Evaluation of Graphs on Surfaces for State-Sum Models with Defects. Julian Farnsteiner and Christoph Schweigert. SIGMA 20 (2024), 102, 51 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2026-03-16T23:40:52Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212790 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T23:40:52Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Farnsteiner, Julian Schweigert, Christoph 2026-02-11T10:40:17Z 2024 The Evaluation of Graphs on Surfaces for State-Sum Models with Defects. Julian Farnsteiner and Christoph Schweigert. SIGMA 20 (2024), 102, 51 pages 1815-0659 2020 Mathematics Subject Classification: 18M30; 18M20; 81T45 arXiv:2312.01946 https://nasplib.isofts.kiev.ua/handle/123456789/212790 https://doi.org/10.3842/SIGMA.2024.102 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. We are grateful to Catherine Meusburger and Alexis Virelizier for detailed discussions and to Alexis Virelizier for insisting that extruded graphs can be dealt with as two-dimensional objects. We thank David Jaklitsch for helpful discussions and Katrin Suchowski for creating the pictures. The authors are supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under SCHW1162/6-1; CS is partially supported under Germany’s Excellence Strategy- EXC 2121 “Quantum Universe”- 390833306. Finally, we thank the anonymous referees for their thorough reviews of the submission, which helped to improve the exposition of the results. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Evaluation of Graphs on Surfaces for State-Sum Models with Defects Article published earlier |
| spellingShingle | The Evaluation of Graphs on Surfaces for State-Sum Models with Defects Farnsteiner, Julian Schweigert, Christoph |
| title | The Evaluation of Graphs on Surfaces for State-Sum Models with Defects |
| title_full | The Evaluation of Graphs on Surfaces for State-Sum Models with Defects |
| title_fullStr | The Evaluation of Graphs on Surfaces for State-Sum Models with Defects |
| title_full_unstemmed | The Evaluation of Graphs on Surfaces for State-Sum Models with Defects |
| title_short | The Evaluation of Graphs on Surfaces for State-Sum Models with Defects |
| title_sort | evaluation of graphs on surfaces for state-sum models with defects |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212790 |
| work_keys_str_mv | AT farnsteinerjulian theevaluationofgraphsonsurfacesforstatesummodelswithdefects AT schweigertchristoph theevaluationofgraphsonsurfacesforstatesummodelswithdefects AT farnsteinerjulian evaluationofgraphsonsurfacesforstatesummodelswithdefects AT schweigertchristoph evaluationofgraphsonsurfacesforstatesummodelswithdefects |