A REMARK ON GEL'FAND DUALITY FOR SPECTRAL TRIPLES

• Bertozzini, Paolo (Department of Mathematics and Statistics Faculty of Science and Technology Thammsat University - Rangsit Campus) ;
• Conti, Roberto (Mathematics School of Mathematical and Physical Sciences University of Newcastle) ;
• Lewkeeratiyutkul, Wicharn (Department of Mathematics Faculty of Science Chulalongkorn University)
• Published : 2011.05.31

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 [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.

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