We prove the -spin cobordism hypothesis in the setting of (weak) 2-categories for every positive integer : the 2-groupoid of 2-dimensional fully extended -spin TQFTs with given target is equivalent to the homotopy fixed points of an induced -action. In particular, such TQFTs are classified by fully dualisable objects together with a trivialisation of the th power of their Serre automorphisms. For , we recover the oriented case (on which our proof builds), while ordinary spin structures correspond to .
To construct examples, we explicitly describe -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.
Cite this article
Nils Carqueville, Lóránt Szegedy, Fully extended -spin TQFTs. Quantum Topol. 14 (2023), no. 3, pp. 467–532DOI 10.4171/QT/193