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arXiv · 0812.3584

A Remark on Gelfand Duality for Spectral Triples

Paolo Bertozzini·Roberto Conti·Wicharn Lewkeeratiyutkul
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Abstract

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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Paolo Bertozzini, Roberto Conti, Wicharn Lewkeeratiyutkul. 2011-12-27. A Remark on Gelfand Duality for Spectral Triples. https://arxiv.org/abs/0812.3584

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