Reconstruction of manifolds in noncommutative geometry
arXiv:math/0610418
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
References in corpus (7)
- Gravity coupled with matter and foundation of non-commutative geometry
- Metrics on states from actions of compact groups
- The Standard Model as a noncommutative geometry: the low energy regime
- Dixmier Traces as Singular Symmetric Functionals and Applications to Measurable Operators
- Connes' Model Building Kit
- Partitions of unity
- A walk in the noncommutative garden
Cited by in corpus (28)
- Riemannian manifolds in noncommutative geometry
- Dynamical Systems on Spectral Metric Spaces
- On the spectral characterization of manifolds
- A unitary invariant in Riemannian geometry
- Noncommutative Geometries and Gravity
- Almost-Commutative Geometries Beyond the Standard Model III: Vector Doublets
- Notes on "quantum gravity" and non-commutative geometry
- Metrics and causality on Moyal planes
- Zeta functions that hear the shape of a Riemann surface
- Modular Theory, Non-Commutative Geometry and Quantum Gravity
- A reconstruction theorem for Connes-Landi deformations of commutative spectral triples
- Elements of noncommutative geometry in inverse problems on manifolds
- C*-algebras of Holonomy-Diffeomorphisms & Quantum Gravity I
- A walk in the noncommutative garden
- On multimatrix models motivated by random noncommutative geometry II: A Yang-Mills-Higgs matrix model
- Coupling of gravity to matter, spectral action and cosmic topology
- On the noncommutative standard model
- Semifinite spectral triples associated with graph C*-algebras
- Computing the spectral action for fuzzy geometries: from random noncommutative geometry to bi-tracial multimatrix models
- Spinors and Theta Deformations
- Quantum gravity: unification of principles and interactions, and promises of spectral geometry
- Remarks on Morphisms of Spectral Geometries
- Contractive spectral triples for crossed products
- Deformations of the Canonical Commutation Relations and Metric Structures
- Noncommutative Geometry and Quantum Group Symmetries
- Solvmanifolds and noncommutative tori with real multiplication
- First numerical approach to a Grosse-Wulkenhaar model
- MSc Thesis: Presentation of Certain New Trends in Noncommutative Geometry