On the spectral characterization of manifolds

By Alain Connes. 2008

301 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4510e566cc67c8496a1180b04c91b232623fe59a

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In Algebra and Number Theory

1. Matilde Marcolli
2. J. Bellissard
3. Kamran Reihani

In Applied Mathematics

1. Matilde Marcolli
2. J. Bellissard
3. Kamran Reihani

In Mathematical Physics

1. Matilde Marcolli
2. J. Bellissard
3. Kamran Reihani
4. Yuri I. Manin

Citations in the corpus

• Regularity and dimension spectrum of the equivariant spectral triple for the odd dimensional quantum spheres (2008, unknown): “3 ([6]).”
• Dynamical Systems on Spectral Metric Spaces (2010, methodology): “The reconstruction problem for Riemannian manifold has been considered by Rennie [58], Rennie and Varilly [59] and Connes [23].”