Classification of spin structures on the noncommutative n-torus

Jan Jitse Venselaar

Classification of spin structures on the noncommutative n-torus

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arxiv 1003.5156 v4 pith:XFENTF6Q submitted 2010-03-26 math.OA math-phmath.MPmath.QA

Jan Jitse Venselaar This is my paper · ORCID

classification math.OAmath-phmath.MPmath.QA

keywords spinstructuresn-torusnoncommutativeclassificationadditionclassifycommutative

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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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Finite spectral triples for the fuzzy torus
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A finite spectral triple for the fuzzy torus is constructed whose Dirac spectrum is the q-integer analogue of the commutative flat torus spectrum, for all four spin structures.

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