[{"ddc":["530"],"isi":1,"external_id":{"isi":["001104620800003"]},"abstract":[{"lang":"eng","text":"We prove the r-spin cobordism hypothesis in the setting of (weak) 2-categories for every positive integer r: the 2-groupoid of 2-dimensional fully extended r-spin TQFTs with given target is equivalent to the homotopy fixed points of an induced Spin 2r -action. In particular, such TQFTs are classified by fully dualisable objects together with a trivialisation of the rth power of their Serre automorphisms. For r=1, we recover the oriented case (on which our proof builds), while ordinary spin structures correspond to r=2.\r\nTo construct examples, we explicitly describe Spin 2r​-homotopy fixed points in the equivariant completion of any symmetric monoidal 2-category. We also show that every object in a 2-category of Landau–Ginzburg models gives rise to fully extended spin TQFTs and that half of these do not factor through the oriented bordism 2-category."}],"date_updated":"2026-07-06T11:52:15Z","department":[{"_id":"MiLe"}],"date_published":"2023-10-16T00:00:00Z","publisher":"EMS Press","license":"https://creativecommons.org/licenses/by/4.0/","issue":"3","language":[{"iso":"eng"}],"oa_version":"Published Version","citation":{"apa":"Carqueville, N., &#38; Szegedy, L. (2023). Fully extended r-spin TQFTs. <i>Quantum Topology</i>. EMS Press. <a href=\"https://doi.org/10.4171/qt/193\">https://doi.org/10.4171/qt/193</a>","ama":"Carqueville N, Szegedy L. Fully extended r-spin TQFTs. <i>Quantum Topology</i>. 2023;14(3):467-532. doi:<a href=\"https://doi.org/10.4171/qt/193\">10.4171/qt/193</a>","short":"N. Carqueville, L. Szegedy, Quantum Topology 14 (2023) 467–532.","ista":"Carqueville N, Szegedy L. 2023. Fully extended r-spin TQFTs. Quantum Topology. 14(3), 467–532.","mla":"Carqueville, Nils, and Lorant Szegedy. “Fully Extended R-Spin TQFTs.” <i>Quantum Topology</i>, vol. 14, no. 3, EMS Press, 2023, pp. 467–532, doi:<a href=\"https://doi.org/10.4171/qt/193\">10.4171/qt/193</a>.","chicago":"Carqueville, Nils, and Lorant Szegedy. “Fully Extended R-Spin TQFTs.” <i>Quantum Topology</i>. EMS Press, 2023. <a href=\"https://doi.org/10.4171/qt/193\">https://doi.org/10.4171/qt/193</a>.","ieee":"N. Carqueville and L. Szegedy, “Fully extended r-spin TQFTs,” <i>Quantum Topology</i>, vol. 14, no. 3. EMS Press, pp. 467–532, 2023."},"corr_author":"1","author":[{"last_name":"Carqueville","first_name":"Nils","full_name":"Carqueville, Nils"},{"orcid":"0000-0003-2834-5054","full_name":"Szegedy, Lorant","id":"7943226E-220E-11EA-94C7-D59F3DDC885E","first_name":"Lorant","last_name":"Szegedy"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"14756","doi":"10.4171/qt/193","publication_identifier":{"issn":["1663-487X"]},"article_type":"original","oa":1,"has_accepted_license":"1","file_date_updated":"2024-01-09T09:25:34Z","publication_status":"published","year":"2023","type":"journal_article","status":"public","quality_controlled":"1","das_tickbox":"1","title":"Fully extended r-spin TQFTs","page":"467-532","intvolume":"        14","keyword":["Geometry and Topology","Mathematical Physics"],"volume":14,"file":[{"success":1,"access_level":"open_access","checksum":"b0590aff6e7ec89cc149ba94d459d3a3","date_created":"2024-01-09T09:25:34Z","creator":"dernst","file_id":"14764","relation":"main_file","date_updated":"2024-01-09T09:25:34Z","content_type":"application/pdf","file_size":707344,"file_name":"2023_QuantumTopol_Carqueville.pdf"}],"article_processing_charge":"Yes","month":"10","tmp":{"short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"day":"16","scopus_import":"1","date_created":"2024-01-08T13:14:48Z","acknowledgement":"N.C. is supported by the DFG Heisenberg Programme.\r\nWe are grateful to Tobias Dyckerhoff, Lukas Müller, Ingo Runkel, and Christopher Schommer-Pries for helpful discussions.","publication":"Quantum Topology"}]