Fully extended r-spin TQFTs Carqueville, Nils Szegedy, Lorant ; https://orcid.org/0000-0003-2834-5054 Geometry and Topology Mathematical Physics ddc:530 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. European Mathematical Society 2023 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/14756 https://research-explorer.ista.ac.at/download/14756/14764 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> eng info:eu-repo/semantics/altIdentifier/doi/10.4171/qt/193 info:eu-repo/semantics/altIdentifier/issn/1663-487X info:eu-repo/semantics/altIdentifier/wos/001104620800003 info:eu-repo/semantics/openAccess