A Framework for Geometric Field Theories and Their Classification in Dimension One
In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such geometric structures, so that it makes sense to require the out...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211351 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Framework for Geometric Field Theories and Their Classification in Dimension One. Matthias Ludewig and Augusto Stoffel. SIGMA 17 (2021), 072, 58 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862555460410802176 |
|---|---|
| author | Ludewig, Matthias Stoffel, Augusto |
| author_facet | Ludewig, Matthias Stoffel, Augusto |
| citation_txt | A Framework for Geometric Field Theories and Their Classification in Dimension One. Matthias Ludewig and Augusto Stoffel. SIGMA 17 (2021), 072, 58 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such geometric structures, so that it makes sense to require the output of our field theory to depend smoothly on the input. We then test our framework on the case of 1-dimensional field theories (with or without orientation) over a manifold . Here, the expectation is that such a field theory is equivalent to the data of a vector bundle over with connection and, in the nonoriented case, the additional data of a nondegenerate bilinear pairing; we prove that this is indeed the case in our framework.
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| first_indexed | 2026-03-13T06:36:38Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211351 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T06:36:38Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ludewig, Matthias Stoffel, Augusto 2025-12-30T15:54:03Z 2021 A Framework for Geometric Field Theories and Their Classification in Dimension One. Matthias Ludewig and Augusto Stoffel. SIGMA 17 (2021), 072, 58 pages 1815-0659 2020 Mathematics Subject Classification: 57R56; 14D21; 57R22 arXiv:2001.05721 https://nasplib.isofts.kiev.ua/handle/123456789/211351 https://doi.org/10.3842/SIGMA.2021.072 In this paper, we develop a general framework of geometric functorial field theories, meaning that all bordisms in question are endowed with geometric structures. We take particular care to establish a notion of smooth variation of such geometric structures, so that it makes sense to require the output of our field theory to depend smoothly on the input. We then test our framework on the case of 1-dimensional field theories (with or without orientation) over a manifold . Here, the expectation is that such a field theory is equivalent to the data of a vector bundle over with connection and, in the nonoriented case, the additional data of a nondegenerate bilinear pairing; we prove that this is indeed the case in our framework. We thank Dmitri Pavlov, Peter Teichner, Konrad Waldorf, and, especially, Stephan Stolz for helpful discussions. We are further indebted to the Max Planck Institute for Mathematics in Bonn and the University of Greifswald, where part of this research was conducted. The first-named author was partially supported by the ARC Discovery Project grant FL170100020 under Chief Investigator and Australian Laureate Fellow Mathai Varghese. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Framework for Geometric Field Theories and Their Classification in Dimension One Article published earlier |
| spellingShingle | A Framework for Geometric Field Theories and Their Classification in Dimension One Ludewig, Matthias Stoffel, Augusto |
| title | A Framework for Geometric Field Theories and Their Classification in Dimension One |
| title_full | A Framework for Geometric Field Theories and Their Classification in Dimension One |
| title_fullStr | A Framework for Geometric Field Theories and Their Classification in Dimension One |
| title_full_unstemmed | A Framework for Geometric Field Theories and Their Classification in Dimension One |
| title_short | A Framework for Geometric Field Theories and Their Classification in Dimension One |
| title_sort | framework for geometric field theories and their classification in dimension one |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211351 |
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