The Gromov-Hausdorff propinquity for metric spectral triples

DOI10.1016/j.aim.2022.108393zbMath1500.46055arXiv1811.10843OpenAlexW4225674112MaRDI QIDQ2671894

Frédéric Latrémolière

Publication date: 3 June 2022

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.10843

zbMATH Keywords

spectral triplesGromov-Hausdorff convergence\(C^*\)-dynamical systemslip-normsMonge-Kantorovich distancenoncommutative metric geometryquantum metric spacesproper monoidsGromov-Hausdorff distance for proper monoids

Mathematics Subject Classification ID

Noncommutative geometry (à la Connes) (58B34) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89) States of selfadjoint operator algebras (46L30)

Related Items (9)

The strongly Leibniz property and the Gromov-Hausdorff propinquity ⋮ Isometry groups of inductive limits of metric spectral triples and Gromov–Hausdorff convergence ⋮ A comparison of two quantum distances ⋮ Sobolev algebras on Lie groups and noncommutative geometry ⋮ Finiteness of metrics on state spaces ⋮ Dirac operators for matrix algebras converging to coadjoint orbits ⋮ Convergence of inductive sequences of spectral triples for the spectral propinquity ⋮ Gromov-Hausdorff convergence of spectral truncations for tori ⋮ The Fell topology and the modular Gromov-Hausdorff propinquity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Equivalence of quantum metrics with a common domain
• The dual Gromov-Hausdorff propinquity
• The Gromov-Hausdorff metric on the space of compact metric spaces is strictly intrinsic
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Metrics on states from actions of compact groups
• Noncommutative geometry and matrix theory: Compactification on tori
• String theory and noncommutative geometry
• Differentiable absorption of Hilbert \(C^\ast\)-modules, connections, and lifts of unbounded operators
• The Podleś sphere as a spectral metric space
• Convergence of Cauchy sequences for the covariant Gromov-Hausdorff propinquity
• Perturbation theory for linear operators.
• Metrics on state spaces
• The quantum structure of spacetime of the Planck scale and quantum fields
• Quantum locally compact metric spaces
• Metric approximations of spectral triples on the Sierpiński gasket and other fractal curves
• The dual modular Gromov-Hausdorff propinquity and completeness
• Convergence of spectral triples on fuzzy tori to spectral triples on quantum tori
• Unbounded bivariant \(K\)-theory and correspondences in noncommutative geometry
• Actions of categories by Lipschitz morphisms on limits for the Gromov-Hausdorff propinquity
• Spectral flow and the unbounded Kasparov product
• Generalized fuzzy torus and its modular properties
• Spectral geometry with a cut-off: topological and metric aspects
• Bounded-Lipschitz distances on the state space of a \(C^*\)-algebra
• Dirac operators and spectral triples for some fractal sets built on curves
• Approximation of quantum tori by finite quantum tori for the quantum Gromov--Hausdorff distance
• Quantum ultrametrics on AF algebras and the Gromov–Hausdorff propinquity
• Matrix geometries and fuzzy spaces as finite spectral triples
• Convergence of Fuzzy Tori and Quantum Tori for the quantum Gromov-Hausdorff Propinquity: an explicit approach
• Quantum Metric Spaces and the Gromov-Hausdorff Propinquity
• Metrics and causality on Moyal planes
• The triangle inequality and the dual Gromov-Hausdorff propinquity
• Leibniz seminorms for "Matrix algebras converge to the sphere"
• Heisenberg Modules over Quantum 2-tori are Metrized Quantum Vector Bundles
• The quantum Gromov-Hausdorff propinquity
• Curved noncommutative tori as Leibniz quantum compact metric spaces
• Deformation quantization for actions of 𝑅^{𝑑}
• Gromov-Hausdorff distance for quantum metric spaces
• A compactness theorem for the dual Gromov-Hausdorff propinquity
• CONNES DISTANCE BY EXAMPLES: HOMOTHETIC SPECTRAL METRIC SPACES
• Some applications of conditional expectations to convergence for the quantum Gromov–Hausdorff propinquity
• The modular Gromov–Hausdorff propinquity
• The covariant Gromov–Hausdorff propinquity
• Higher weak derivatives and reflexive algebras of operators
• Matricial bridges for “Matrix algebras converge to the sphere”
• Compact metric spaces, Fredholm modules, and hyperfiniteness
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
• Noncommutative gauge theory on fuzzy sphere from matrix model

This page was built for publication: The Gromov-Hausdorff propinquity for metric spectral triples