Obstructions to matricial stability of discrete groups and almost flat $K$-theory

DOI10.1016/j.aim.2021.107722zbMath1477.19005arXiv2007.12655OpenAlexW3149298710MaRDI QIDQ2237357

Marius Dǎdǎrlat

Publication date: 27 October 2021

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

Full work available at URL: https://arxiv.org/abs/2007.12655

zbMATH Keywords

quasidiagonal \(C^*\)-algebraalmost flat bundlesapproximate representations\(\gamma\)-elementmatricial stability

Mathematics Subject Classification ID

Geometric group theory (20F65) (K)-theory and operator algebras (including cyclic theory) (46L80) Kasparov theory ((KK)-theory) (19K35)

Related Items (5)

Quasi-representations of groups and two-homology ⋮ On amenable Hilbert-Schmidt stable groups ⋮ Frobenius non-stability of nilpotent groups ⋮ \(\mathrm{C}^\ast\)-algebras. Abstracts from the workshop held August 7--13, 2022 ⋮ Stability and instability of lattices in semisimple groups

Cites Work

• Unnamed Item
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• On unital full amalgamated free products of quasidiagonal \(C^\ast\)-algebras
• On groups with quasidiagonal \(C^\ast\)-algebras
• The Picard group of the moduli space of curves with level structures
• E-theory for \(C^*\)-algebras over topological spaces
• Quasidiagonality of nuclear \(\mathrm{C}^\ast\)-algebras
• Deformations of nilpotent groups and homotopy symmetric \(C^*\)-algebras
• Connective \(C^{\ast}\)-algebras
• Hearing the platycosms
• Geometry of the mapping class groups. I: Boundary amenability
• Research announcement: The structure of groups with a quasiconvex hierarchy.
• Examples of hyperlinear groups without factorization property
• On \(\varepsilon\)-representations
• Equivariant KK-theory and the Novikov conjecture
• Une notion de nucléarité en K-théorie (d'après J. Cuntz). (A notion of nuclearity in K-theory (in the sense of J. Cuntz))
• Baumslag-Solitar groups and some other groups of cohomological dimension two
• Invariants of almost commuting unitaries
• Groups acting on buildings, operator \(K\)-theory, and Novikov's conjecture
• On the spectrum of the sum of generators for a finitely generated group
• \(K\)-theory for \(C^*\)-algebras of one-relator groups
• Discrete groups with Kazhdan's property \(T\) and factorization property are residually finite
• Generalized inductive limits of finite-dimensional \(C^*\)-algebras
• Quasidiagonal morphisms and homotopy
• Groups acting properly on ``bolic spaces and the Novikov conjecture
• Residual amenability and the approximation of \(L^2\)-invariants
• The coarse Baum-Connes conjecture and groupoids
• The topology and geometry of automorphism groups of free groups
• Almost flat \(K\)-theory of classifying spaces
• MF-property for countable discrete groups
• Permanence properties of \(C^*\)-exact groups
• A universal multicoefficient theorem for the Kasparov groups
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• The relative Mishchenko-Fomenko higher index and almost flat bundles. I: The relative Mishchenko-Fomenko index
• Groups with Spanier-Whitehead duality
• \(C^\ast\)-stability of discrete groups
• Subalgebras of simple AF-algebras
• Cohomological obstructions to lifting properties for full C*-algebras of property (T) groups
• A non-LEA sofic group
• The Novikov conjecture for linear groups
• \(K\)-theory for group \(C^*\)-algebras and semigroup \(C^*\)-algebras
• Extended abstracts fall 2012. Automorphisms of free groups. Selected papers based on the presentations at the CRM research program ``Automorphisms of free groups: algorithms, geometry and dynamics, Barcelona, Spain, fall 2012.
• Group quasi-representations and almost flat bundles
• The characteristic homomorphism of flat bundles
• Free subgroups in linear groups
• Remarks on Yu’s ‘property A’ for discrete metric spaces and groups
• Exactness of one relator groups
• Quasi-representations of surface groups
• GROUP QUASI-REPRESENTATIONS AND INDEX THEORY
• Orthogonale Gruppen über algebraischen Zahlkörpern.
• Invariant means and finite representation theory of 𝐶*-algebras
• On the Residual Finiteness of Certain Mapping Class Groups
• Rational cohomology of nilpotent groups and lie algebras
• The second homology groups of mapping class groups of orientable surfaces
• On embeddings of full amalgamated free product C*–algebras
• Shape theory for $C^*$-algebras.
• Constructions preserving Hilbert space uniform embeddability of discrete groups
• A note on full free product C*-algebras, lifting and quasidiagonality
• FINITARY APPROXIMATIONS OF GROUPS AND THEIR APPLICATIONS
• STABILITY, COHOMOLOGY VANISHING, AND NONAPPROXIMABLE GROUPS
• Automorphism Groups of Residually Finite Groups
• Deformations of wreath products
• The mapping class group from the viewpoint of measure equivalence theory
• Residual Finiteness of Surface Groups
• Nonresidually Finite One-Relator Groups
• Cohomology Theory of Lie Groups and Lie Algebras
• Permanence properties of the Baum-Connes conjecture
• \(E\)-theory and \(KK\)-theory for groups which act properly and isometrically on Hilbert space
• Asymptotic unitary equivalence in \(KK\)-theory
• Groups with the Haagerup property. Gromov's a-T-menability

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