State sum construction of two-dimensional topological quantum field theories on spin surfaces

Understand

We provide a combinatorial model for spin surfaces.

• Given a triangulation of an oriented surface, a spin structure is encoded by assigning to each triangle a preferred edge, and to each edge an orientation and a sign, subject to certain admissibility conditions.
• The behaviour of this data under Pachner moves is then used to define a state sum topological field theory on spin surfaces.
• The algebraic data is a Delta-separable Frobenius algebra whose Nakayama automorphism is an involution.