A REMARK ON GEL'FAND DUALITY FOR SPECTRAL TRIPLES

Title & Authors
A REMARK ON GEL'FAND DUALITY FOR SPECTRAL TRIPLES
Bertozzini, Paolo; Conti, Roberto; Lewkeeratiyutkul, Wicharn;

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-$\small{C^*}$-algebras. We also construct an embedding of a "quotient" of the category of spectral triples introduced in [5] 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.
Keywords
spectral triple;spin manifold;category;
Language
English
Cited by
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