{"publisher":"European Mathematical Society","publication_status":"published","date_created":"2024-01-08T13:14:48Z","month":"10","issue":"3","publication":"Quantum Topology","date_updated":"2024-01-09T09:27:46Z","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"MiLe"}],"doi":"10.4171/qt/193","oa_version":"Published Version","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.","file_date_updated":"2024-01-09T09:25:34Z","file":[{"relation":"main_file","file_id":"14764","content_type":"application/pdf","file_name":"2023_QuantumTopol_Carqueville.pdf","checksum":"b0590aff6e7ec89cc149ba94d459d3a3","date_created":"2024-01-09T09:25:34Z","file_size":707344,"success":1,"date_updated":"2024-01-09T09:25:34Z","creator":"dernst","access_level":"open_access"}],"_id":"14756","article_type":"original","status":"public","keyword":["Geometry and Topology","Mathematical Physics"],"year":"2023","oa":1,"abstract":[{"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.","lang":"eng"}],"page":"467-532","author":[{"first_name":"Nils","last_name":"Carqueville","full_name":"Carqueville, Nils"},{"full_name":"Szegedy, Lorant","id":"7943226E-220E-11EA-94C7-D59F3DDC885E","first_name":"Lorant","last_name":"Szegedy","orcid":"0000-0003-2834-5054"}],"language":[{"iso":"eng"}],"day":"16","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"has_accepted_license":"1","publication_identifier":{"issn":["1663-487X"]},"ddc":["530"],"intvolume":"        14","citation":{"mla":"Carqueville, Nils, and Lorant Szegedy. “Fully Extended R-Spin TQFTs.” <i>Quantum Topology</i>, vol. 14, no. 3, European Mathematical Society, 2023, pp. 467–532, doi:<a href=\"https://doi.org/10.4171/qt/193\">10.4171/qt/193</a>.","ista":"Carqueville N, Szegedy L. 2023. Fully extended r-spin TQFTs. Quantum Topology. 14(3), 467–532.","ieee":"N. Carqueville and L. Szegedy, “Fully extended r-spin TQFTs,” <i>Quantum Topology</i>, vol. 14, no. 3. European Mathematical Society, pp. 467–532, 2023.","short":"N. Carqueville, L. Szegedy, Quantum Topology 14 (2023) 467–532.","chicago":"Carqueville, Nils, and Lorant Szegedy. “Fully Extended R-Spin TQFTs.” <i>Quantum Topology</i>. European Mathematical Society, 2023. <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>","apa":"Carqueville, N., &#38; Szegedy, L. (2023). Fully extended r-spin TQFTs. <i>Quantum Topology</i>. European Mathematical Society. <a href=\"https://doi.org/10.4171/qt/193\">https://doi.org/10.4171/qt/193</a>"},"title":"Fully extended r-spin TQFTs","article_processing_charge":"Yes","scopus_import":"1","date_published":"2023-10-16T00:00:00Z","volume":14,"quality_controlled":"1"}