# Topological field theory on r-spin surfaces and the Arf-invariant

@article{Runkel2021TopologicalFT, title={Topological field theory on r-spin surfaces and the Arf-invariant}, author={Ingo Runkel and L'or'ant Szegedy}, journal={Journal of Mathematical Physics}, year={2021} }

We give a combinatorial model for r-spin surfaces with parametrised boundary based on Novak (2015). The r-spin structure is encoded in terms of $\mathbb{Z}_r$-valued indices assigned to the edges of a polygonal decomposition. With the help of this model we count the number of mapping class group orbits on r-spin surfaces with parametrised boundary and fixed r-spin structure on each boundary component, extending (and giving a different proof of) results in Geiges, Gonzalo (2012) and Randal…

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