Classification of spin structures on the noncommutative n-torus

Details Classification of spin structures on the noncommutative n-torus Classification of spin structures on the noncommutative n-torus

2010-03-26

arxiv.org/abs/1003.5156v4

Mathematics

Operator Algebras

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

Scientific paper

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.

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