Reconstructing manifolds from truncations of spectral triples

Abstract We explore the geometric implications of introducing a spectral cut-off on compact Riemannian manifolds. This is naturally phrased in framework non-commutative geometry, where we work with triples that are truncated by projections Dirac-type operators. associate metric space ‘localized’ states to each truncation. The Gromov–Hausdorff limit these spaces then shown equal underlying manifold one started with. leads us propose computational algorithm allows approximate from finite-dimensional data. subsequently develop technique for embedding resulting graphs Euclidean asymptotically recover an isometric limit. test algorithms truncation sphere and recently investigated perturbation thereof.