article published yes Nils Carqueville author Lorant Szegedy author 7943226E-220E-11EA-94C7-D59F3DDC885E0000-0003-2834-5054 MiLe department 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. To 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. https://research-explorer.ista.ac.at/download/14756/14764/2023_QuantumTopol_Carqueville.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ European Mathematical Society2023 eng Geometry and TopologyMathematical Physics 1663-487X 00110462080000310.4171/qt/193 143467-532 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>. N. Carqueville, L. Szegedy, Quantum Topology 14 (2023) 467–532. 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> 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>. Carqueville N, Szegedy L. 2023. Fully extended r-spin TQFTs. Quantum Topology. 14(3), 467–532. 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. 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> 147562024-01-08T13:14:48Z2025-09-09T14:16:16Z