Topological field theory on rspin surfaces and the Arf invariant
Abstract
We give a combinatorial model for rspin surfaces with parametrised boundary based on Novak (2015). The rspin 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 twodimensional topological field theories on rspin surfaces. We show that an example of such a topological field theory computes the Arfinvariant of an rspin surface as introduced in Geiges, Gonzalo (2012) and RandalWilliams (2014). This implies in particular that the rspin Arfinvariant is constant on orbits of the mapping class group, providing an alternative proof of that fact.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.09978
 Bibcode:
 2018arXiv180209978R
 Keywords:

 Mathematics  Quantum Algebra;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Geometric Topology
 EPrint:
 v2: 52 pages, removed classification of mapping class group orbits as suggested by referee, version to appear in Journal of Mathematical Physics