Fully extended r-spin TQFTs

Carqueville N, Szegedy L. 2023. Fully extended r-spin TQFTs. Quantum Topology. 14(3), 467–532.

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Journal Article | Published | English

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Author
Carqueville, Nils; Szegedy, LorantISTA
Department
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.
Publishing Year
Date Published
2023-10-16
Journal Title
Quantum Topology
Publisher
European Mathematical Society
Acknowledgement
N.C. is supported by the DFG Heisenberg Programme. We are grateful to Tobias Dyckerhoff, Lukas Müller, Ingo Runkel, and Christopher Schommer-Pries for helpful discussions.
Volume
14
Issue
3
Page
467-532
ISSN
IST-REx-ID

Cite this

Carqueville N, Szegedy L. Fully extended r-spin TQFTs. Quantum Topology. 2023;14(3):467-532. doi:10.4171/qt/193
Carqueville, N., & Szegedy, L. (2023). Fully extended r-spin TQFTs. Quantum Topology. European Mathematical Society. https://doi.org/10.4171/qt/193
Carqueville, Nils, and Lorant Szegedy. “Fully Extended R-Spin TQFTs.” Quantum Topology. European Mathematical Society, 2023. https://doi.org/10.4171/qt/193.
N. Carqueville and L. Szegedy, “Fully extended r-spin TQFTs,” Quantum Topology, vol. 14, no. 3. European Mathematical Society, pp. 467–532, 2023.
Carqueville N, Szegedy L. 2023. Fully extended r-spin TQFTs. Quantum Topology. 14(3), 467–532.
Carqueville, Nils, and Lorant Szegedy. “Fully Extended R-Spin TQFTs.” Quantum Topology, vol. 14, no. 3, European Mathematical Society, 2023, pp. 467–532, doi:10.4171/qt/193.
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2024-01-09
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