{"issue":"10","author":[{"first_name":"Ingo","full_name":"Runkel, Ingo","last_name":"Runkel"},{"id":"7943226E-220E-11EA-94C7-D59F3DDC885E","orcid":"0000-0003-2834-5054","full_name":"Szegedy, Lorant","first_name":"Lorant","last_name":"Szegedy"}],"article_processing_charge":"No","oa":1,"intvolume":"        62","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"MiLe"}],"doi":"10.1063/5.0037826","date_updated":"2023-08-14T08:04:12Z","publication_identifier":{"issn":["00222488"]},"abstract":[{"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 ℤ𝑟-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.","lang":"eng"}],"date_published":"2021-10-01T00:00:00Z","_id":"10176","external_id":{"arxiv":["1802.09978"],"isi":["000755638500010"]},"publication":"Journal of Mathematical Physics","status":"public","article_type":"original","volume":62,"day":"01","isi":1,"scopus_import":"1","type":"journal_article","publisher":"AIP Publishing","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1802.09978"}],"language":[{"iso":"eng"}],"month":"10","publication_status":"published","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.”","quality_controlled":"1","article_number":"102302","title":"Topological field theory on r-spin surfaces and the Arf-invariant","date_created":"2021-10-24T22:01:32Z","year":"2021","citation":{"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.","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>","ista":"Runkel I, Szegedy L. 2021. Topological field theory on r-spin surfaces and the Arf-invariant. Journal of Mathematical Physics. 62(10), 102302.","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>.","short":"I. Runkel, L. Szegedy, Journal of Mathematical Physics 62 (2021).","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>","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>."}}