Classification of spin structures on the noncommutative n-torus

Understand

We classify spin structures on the noncommutative torus, and find that the noncommutative n-torus has 2^n spin structures, corresponding to isospectral deformations of spin structures on the commutative n-torus.

• For n>3 the classification depends on Connes' spin manifold theorem.
• In addition, we study unitary equivalences of these spin structures.