Almost commuting matrices, cohomology, and dimension

DOI10.24033/asens.2563arXiv1902.10451OpenAlexW2922119167MaRDI QIDQ6131434

Tatiana Shulman, Dominic Enders

Publication date: 5 April 2024

Published in: Annales Scientifiques de l'École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.10451

zbMATH Keywords

\(K\)-theory\(C^{*}\)-algebraCalkin algebraalmost commuting matrices

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) General theory of (C^*)-algebras (46L05)

Cites Work

• Topological insulators and \(C^{*}\)-algebras: theory and numerical practice
• On covering dimension and inverse limits of compact spaces
• Almost commuting matrices and a quantitative version of the Brown- Douglas-Fillmore theorem
• The noncommutative topology of one-dimensional spaces
• The completely positive lifting problem for \(C^*\)-algebras
• Extensions of \(C^*\)-algebras and \(K\)-homology
• Infinite dimensional compacta containing no \(n\)-dimensional \((n \geq 1)\) subsets
• Lifting solutions to perturbing problems in \(C^*\)-algebras
• Stability of group relations under small Hilbert-Schmidt perturbations
• Approximation with normal operators with finite spectrum, and an elementary proof of a Brown-Douglas-Fillmore theorem.
• \(C^\ast\)-stability of discrete groups
• Which compacta are noncommutative ARs?
• Group stability and property (T)
• A characterization of semiprojectivity for commutative C *-algebras
• The Homotopy Lifting Theorem for Semiprojective $C^*$-Algebras
• Distance to normal elements in 𝐶*-algebras of real rank zero
• Almost commuting Hermitian matrices.
• K-Theory and Asymptotically Commuting Matrices
• Almost Commuting Matrices Need not be Nearly Commuting
• Almost Commuting Unitary Matrices
• Some unsolved problems of unknown depth about operators on Hilbert space
• Almost commuting self-adjoint matrices - a short proof of Huaxin Lin's theorem.
• The Toeplitz algebra has nuclear dimension one
• STABILITY, COHOMOLOGY VANISHING, AND NONAPPROXIMABLE GROUPS
• An Infinite-Dimensional Compactum with no Positive-Dimensional Compact Subsets-A Simpler Construction
• \(C^*\)-algebras by example
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