@article{14756,
  abstract     = {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.},
  author       = {Carqueville, Nils and Szegedy, Lorant},
  issn         = {1663-487X},
  journal      = {Quantum Topology},
  keywords     = {Geometry and Topology, Mathematical Physics},
  number       = {3},
  pages        = {467--532},
  publisher    = {European Mathematical Society},
  title        = {{Fully extended r-spin TQFTs}},
  doi          = {10.4171/qt/193},
  volume       = {14},
  year         = {2023},
}