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- W3204226951 abstract "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." @default.
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- W3204226951 date "2021-10-01" @default.
- W3204226951 modified "2023-10-17" @default.
- W3204226951 title "Topological field theory on <i>r</i>-spin surfaces and the Arf-invariant" @default.
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- W3204226951 doi "https://doi.org/10.1063/5.0037826" @default.
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