On the spectral characterization of manifolds

Understand

We show that the first five of the axioms we had formulated on spectral triples suffice (in a slightly stronger form) to characterize the spectral triples associated to smooth compact manifolds.

• The algebra, which is assumed to be commutative, is shown to be isomorphic to the algebra of all smooth functions on a unique smooth oriented compact manifold, while the operator is shown to be of Dirac type and the metric to be Riemannian.