We present a state-sum construction of topological field theories (TFT)
on r-spin surfaces which uses a combinatorial model of r-spin structures
based on the work of Novak. We give an example of such a TFT which
computes the Arf invariant for r even. We use the combinatorial model
and this TFT to calculate diffeomorphism classes of r-spin surfaces with
parametrized boundary, extending results of Geiges and Gonzalo and of
Randal-Williams.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/3444
[3] http://www.mpim-bonn.mpg.de/de/TopologySeminar