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A REMARK ON GEL'FAND DUALITY FOR SPECTRAL TRIPLES
Bertozzini, Paolo,Conti, Roberto,Lewkeeratiyutkul, Wicharn Korean Mathematical Society 2011 대한수학회보 Vol.48 No.3
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.
A remark on Gel'fand duality for spectral triples
Paolo Bertozzini,Roberto Conti,Wicharn Lewkeeratiyutkul 대한수학회 2011 대한수학회보 Vol.48 No.3
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. 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.