A Remark on Gelfand Duality for Spectral Triples

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Bertozzini, Paolo
Conti, Roberto
Lewkeeratiyutkul, Wicharn
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Abstract
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We present a duality between the category of compact Riemannian spin manifolds (equipped with a given spin bundle and charge conjugation) with isometries as morphisms and a suitable "metric" category of spectral triples over commutative pre-C*-algebras. We also construct an embedding of a "quotient" of the category of spectral triples introduced in arXiv:math/0502583v1 into the latter metric category. Finally we discuss a further related duality in the case of orientation and spin-preserving maps between manifolds of fixed dimension.
Comment: 15 pages, AMS-LaTeX2e, results unchanged, several improvements in the exposition, appendix added
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Mathematics - Operator Algebras, Mathematics - Category Theory, 46L87 (Primary) 46M15, 16F99, 15A66 (Secondary)
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