---
_id: '10176'
abstract:
- lang: eng
  text: "We give a combinatorial model for r-spin surfaces with parameterized boundary
    based on Novak (“Lattice topological field theories in two dimensions,” Ph.D.
    thesis, Universität Hamburg, 2015). The r-spin structure is encoded in terms of
    ℤ\U0001D45F-valued indices assigned to the edges of a polygonal decomposition.
    This combinatorial model is designed for our state-sum construction of two-dimensional
    topological field theories on r-spin surfaces. We show that an example of such
    a topological field theory computes the Arf-invariant of an r-spin surface as
    introduced by Randal-Williams [J. Topol. 7, 155 (2014)] and Geiges et al. [Osaka
    J. Math. 49, 449 (2012)]. This implies, in particular, that the r-spin Arf-invariant
    is constant on orbits of the mapping class group, providing an alternative proof
    of that fact."
acknowledgement: We would like to thank Nils Carqueville, Tobias Dyckerhoff, Jan Hesse,
  Ehud Meir, Sebastian Novak, Louis-Hadrien Robert, Nick Salter, Walker Stern, and
  Lukas Woike for helpful discussions and comments. L.S. was supported by the DFG
  Research Training Group 1670 “Mathematics Inspired by String Theory and Quantum
  Field Theory.”
article_number: '102302'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Ingo
  full_name: Runkel, Ingo
  last_name: Runkel
- first_name: Lorant
  full_name: Szegedy, Lorant
  id: 7943226E-220E-11EA-94C7-D59F3DDC885E
  last_name: Szegedy
  orcid: 0000-0003-2834-5054
citation:
  ama: Runkel I, Szegedy L. Topological field theory on r-spin surfaces and the Arf-invariant.
    <i>Journal of Mathematical Physics</i>. 2021;62(10). doi:<a href="https://doi.org/10.1063/5.0037826">10.1063/5.0037826</a>
  apa: Runkel, I., &#38; Szegedy, L. (2021). Topological field theory on r-spin surfaces
    and the Arf-invariant. <i>Journal of Mathematical Physics</i>. AIP Publishing.
    <a href="https://doi.org/10.1063/5.0037826">https://doi.org/10.1063/5.0037826</a>
  chicago: Runkel, Ingo, and Lorant Szegedy. “Topological Field Theory on R-Spin Surfaces
    and the Arf-Invariant.” <i>Journal of Mathematical Physics</i>. AIP Publishing,
    2021. <a href="https://doi.org/10.1063/5.0037826">https://doi.org/10.1063/5.0037826</a>.
  ieee: I. Runkel and L. Szegedy, “Topological field theory on r-spin surfaces and
    the Arf-invariant,” <i>Journal of Mathematical Physics</i>, vol. 62, no. 10. AIP
    Publishing, 2021.
  ista: Runkel I, Szegedy L. 2021. Topological field theory on r-spin surfaces and
    the Arf-invariant. Journal of Mathematical Physics. 62(10), 102302.
  mla: Runkel, Ingo, and Lorant Szegedy. “Topological Field Theory on R-Spin Surfaces
    and the Arf-Invariant.” <i>Journal of Mathematical Physics</i>, vol. 62, no. 10,
    102302, AIP Publishing, 2021, doi:<a href="https://doi.org/10.1063/5.0037826">10.1063/5.0037826</a>.
  short: I. Runkel, L. Szegedy, Journal of Mathematical Physics 62 (2021).
corr_author: '1'
date_created: 2021-10-24T22:01:32Z
date_published: 2021-10-01T00:00:00Z
date_updated: 2025-07-10T11:49:44Z
day: '01'
department:
- _id: MiLe
doi: 10.1063/5.0037826
external_id:
  arxiv:
  - '1802.09978'
  isi:
  - '000755638500010'
intvolume: '        62'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1802.09978
month: '10'
oa: 1
oa_version: Preprint
publication: Journal of Mathematical Physics
publication_identifier:
  issn:
  - 0022-2488
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Topological field theory on r-spin surfaces and the Arf-invariant
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 62
year: '2021'
...