Non-Semisimple TQFT's and BPS -Series
We propose and, in some cases, prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic . Both types of invariants are labeled by extra data, which plays an important role in the proposed relation. Bridging the two sides - which until rec...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2023 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211874 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Non-Semisimple TQFT's and BPS -Series. Francesco Costantino, Sergei Gukov and Pavel Putrov. SIGMA 19 (2023), 010, 71 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862680757729755136 |
|---|---|
| author | Costantino, Francesco Gukov, Sergei Putrov, Pavel |
| author_facet | Costantino, Francesco Gukov, Sergei Putrov, Pavel |
| citation_txt | Non-Semisimple TQFT's and BPS -Series. Francesco Costantino, Sergei Gukov and Pavel Putrov. SIGMA 19 (2023), 010, 71 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We propose and, in some cases, prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic . Both types of invariants are labeled by extra data, which plays an important role in the proposed relation. Bridging the two sides - which until recently were developed independently, using very different methods - opens many new avenues. In one direction, it allows us to study (and perhaps even to formulate) -series invariants labeled by spinᶜ structures in terms of non-semisimple invariants. In the opposite direction, it offers new insights and perspectives on various elements of non-semisimple TQFT's, bringing the latter into one unifying framework with other invariants of knots and 3-manifolds that recently found realization in quantum field theory and in string theory.
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| first_indexed | 2026-03-17T00:18:23Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211874 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T00:18:23Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Costantino, Francesco Gukov, Sergei Putrov, Pavel 2026-01-14T09:54:52Z 2023 Non-Semisimple TQFT's and BPS -Series. Francesco Costantino, Sergei Gukov and Pavel Putrov. SIGMA 19 (2023), 010, 71 pages 1815-0659 2020 Mathematics Subject Classification: TQFT arXiv:2107.14238 https://nasplib.isofts.kiev.ua/handle/123456789/211874 https://doi.org/10.3842/SIGMA.2023.010 We propose and, in some cases, prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic . Both types of invariants are labeled by extra data, which plays an important role in the proposed relation. Bridging the two sides - which until recently were developed independently, using very different methods - opens many new avenues. In one direction, it allows us to study (and perhaps even to formulate) -series invariants labeled by spinᶜ structures in terms of non-semisimple invariants. In the opposite direction, it offers new insights and perspectives on various elements of non-semisimple TQFT's, bringing the latter into one unifying framework with other invariants of knots and 3-manifolds that recently found realization in quantum field theory and in string theory. We would like to thank Francesco Benini, Christian Copetti, Boris Feigin, Azat Gainutdinov, Hiraku Nakajima, Sunghyuk Park, Du Pei, and Nicolai Reshetikhin for helpful discussions and the anonymous Referees for the valuable suggestions on the improvement of the paper. We also would like to thank the organizers of the 2019 conference “New Developments in Quantum Topology” at UC Berkeley, where the discussion on the relation between the two invariants was initiated. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664227. The work of F.C. was supported by the French Agence Nationale de la Recherche via the ANR Project QUANTACT and by the Labex CIMI ANR-11-LABX-0040. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Non-Semisimple TQFT's and BPS -Series Article published earlier |
| spellingShingle | Non-Semisimple TQFT's and BPS -Series Costantino, Francesco Gukov, Sergei Putrov, Pavel |
| title | Non-Semisimple TQFT's and BPS -Series |
| title_full | Non-Semisimple TQFT's and BPS -Series |
| title_fullStr | Non-Semisimple TQFT's and BPS -Series |
| title_full_unstemmed | Non-Semisimple TQFT's and BPS -Series |
| title_short | Non-Semisimple TQFT's and BPS -Series |
| title_sort | non-semisimple tqft's and bps -series |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211874 |
| work_keys_str_mv | AT costantinofrancesco nonsemisimpletqftsandbpsseries AT gukovsergei nonsemisimpletqftsandbpsseries AT putrovpavel nonsemisimpletqftsandbpsseries |