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

Version accepted for publication in Journal of Noncommutative Geometry. Revised irreducibility condition