A Remark on Gelfand Duality for Spectral Triples

Details A Remark on Gelfand Duality for Spectral Triples A Remark on Gelfand Duality for Spectral Triples

2008-12-18

arxiv.org/abs/0812.3584v2

Bulletin of the Korean Mathematical Society 48 n. 3, 505-521 (2011)

Mathematics

Operator Algebras

15 pages, AMS-LaTeX2e, results unchanged, several improvements in the exposition, appendix added

Scientific paper

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.

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