---
_id: '14756'
abstract:
- lang: eng
  text: "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.\r\nTo 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."
acknowledgement: "N.C. is supported by the DFG Heisenberg Programme.\r\nWe are grateful
  to Tobias Dyckerhoff, Lukas Müller, Ingo Runkel, and Christopher Schommer-Pries
  for helpful discussions."
article_processing_charge: Yes
article_type: original
author:
- first_name: Nils
  full_name: Carqueville, Nils
  last_name: Carqueville
- first_name: Lorant
  full_name: Szegedy, Lorant
  id: 7943226E-220E-11EA-94C7-D59F3DDC885E
  last_name: Szegedy
  orcid: 0000-0003-2834-5054
citation:
  ama: 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>
  apa: 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>
  chicago: 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>.
  ieee: 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.
  ista: Carqueville N, Szegedy L. 2023. Fully extended r-spin TQFTs. Quantum Topology.
    14(3), 467–532.
  mla: 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>.
  short: N. Carqueville, L. Szegedy, Quantum Topology 14 (2023) 467–532.
corr_author: '1'
date_created: 2024-01-08T13:14:48Z
date_published: 2023-10-16T00:00:00Z
date_updated: 2025-09-09T14:16:16Z
day: '16'
ddc:
- '530'
department:
- _id: MiLe
doi: 10.4171/qt/193
external_id:
  isi:
  - '001104620800003'
file:
- access_level: open_access
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  creator: dernst
  date_created: 2024-01-09T09:25:34Z
  date_updated: 2024-01-09T09:25:34Z
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has_accepted_license: '1'
intvolume: '        14'
isi: 1
issue: '3'
keyword:
- Geometry and Topology
- Mathematical Physics
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '10'
oa: 1
oa_version: Published Version
page: 467-532
publication: Quantum Topology
publication_identifier:
  issn:
  - 1663-487X
publication_status: published
publisher: European Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fully extended r-spin TQFTs
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 14
year: '2023'
...