Reconstruction of manifolds in noncommutative geometry

Abstract

We show that the algebra A of a commutative unital spectral triple (A,H,D) satisfying several additional conditions, slightly stronger than those proposed by Connes, is the algebra of smooth functions on a compact spin manifold.

67 pages, no figures, Latex; major changes, a new Appendix A

Cited by in corpus (7)

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• Noncommutative Geometries and Gravity
• Almost-Commutative Geometries Beyond the Standard Model III: Vector Doublets
• On the noncommutative standard model
• Semifinite spectral triples associated with graph C*-algebras
• Quantum gravity: unification of principles and interactions, and promises of spectral geometry
• Solvmanifolds and noncommutative tori with real multiplication