TQFTs have received widespread attention in recent years. In mathematics
for example due to Lurie's proof of the cobordism hypothesis. In physics
they are used as toy models to understand structure, especially
boundaries and defects.
I will present a lattice construction of 2d Spin TFT. This mostly
motivated as both a toy model and stepping stone for a mathematical
construction of rational conformal field theories with fermions.
I will first describe a combinatorial model for spin surfaces that
consists of a triangulation and a finte set of extra data. This model is
then used to construct TFT correlators as morphisms in a symmetric
monoidal category, given a Frobenius algebra as input. The result is
shown to be independent of the triangulation used, and one obtains thus
a 2dTFT.
All results and constructions can be generalised to framed surfaces in a
relatively straightforward way.