Classification of spin structures on the noncommutative n-torus

Abstract

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≥4 the classification depends on Connes’ spin manifold theorem. In addition, we study unitary equivalences of these spin structures.