Cyclic Objects from Surfaces
In this paper, we endow the family of all closed genus ≥ 1 surfaces with a structure of a (co)cyclic object in the category of 3-dimensional cobordisms. As a corollary, any 3-dimensional TQFT induces a (co)cyclic module, which we compute algebraically for the Reshetikhin-Turaev TQFT.
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/214172 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Cyclic Objects from Surfaces. Ivan Bartulović. SIGMA 21 (2025), 074, 44 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862620913207345152 |
|---|---|
| author | Bartulović, Ivan |
| author_facet | Bartulović, Ivan |
| citation_txt | Cyclic Objects from Surfaces. Ivan Bartulović. SIGMA 21 (2025), 074, 44 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we endow the family of all closed genus ≥ 1 surfaces with a structure of a (co)cyclic object in the category of 3-dimensional cobordisms. As a corollary, any 3-dimensional TQFT induces a (co)cyclic module, which we compute algebraically for the Reshetikhin-Turaev TQFT.
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| first_indexed | 2026-03-21T12:21:25Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214172 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T12:21:25Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bartulović, Ivan 2026-02-19T16:04:30Z 2025 Cyclic Objects from Surfaces. Ivan Bartulović. SIGMA 21 (2025), 074, 44 pages 1815-0659 2020 Mathematics Subject Classification: 18N50; 57K16 arXiv:2306.07216 https://nasplib.isofts.kiev.ua/handle/123456789/214172 https://doi.org/10.3842/SIGMA.2025.074 In this paper, we endow the family of all closed genus ≥ 1 surfaces with a structure of a (co)cyclic object in the category of 3-dimensional cobordisms. As a corollary, any 3-dimensional TQFT induces a (co)cyclic module, which we compute algebraically for the Reshetikhin-Turaev TQFT. Most of the content of this paper is part of my PhD thesis. I would like to thank my supervisor, Alexis Virelizier, for his comments and advice. I would also like to thank Ulrich Krähmer, Christoph Schweigert, Kenichi Shimizu, and anonymous referees for discussions and comments. Finally, I am grateful to the Laboratoire Paul Painlevé of the University of Lille and the Institut für Geometrie of the TU Dresden for their hospitality. This work was supported by the Labex CEMPI (ANR-11-LABX-0007-01), by the Région Hauts-de-France, and by the FNS-ANR OChoTop grant (ANR-18-CE93-0002-01). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Cyclic Objects from Surfaces Article published earlier |
| spellingShingle | Cyclic Objects from Surfaces Bartulović, Ivan |
| title | Cyclic Objects from Surfaces |
| title_full | Cyclic Objects from Surfaces |
| title_fullStr | Cyclic Objects from Surfaces |
| title_full_unstemmed | Cyclic Objects from Surfaces |
| title_short | Cyclic Objects from Surfaces |
| title_sort | cyclic objects from surfaces |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214172 |
| work_keys_str_mv | AT bartulovicivan cyclicobjectsfromsurfaces |