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

Understand

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.
• 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 in Geiges, Gonzalo (2012) and Randal-Williams (2014).