On quantitative operator \(K\)-theory

DOI10.5802/aif.2940zbMath1329.19009arXiv1106.2419OpenAlexW2964231843MaRDI QIDQ748389

Hervé Oyono-Oyono, Guo-Liang Yu

Publication date: 20 October 2015

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.2419

zbMATH Keywords

\(K\)-theoryinductive systemBaum-Connes conjecturecontrolled topologyRoe algebrafiltered \(C^*\)-algebra

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Exotic index theories on manifolds (58J22) Kasparov theory ((KK)-theory) (19K35)

Related Items (17)

Tolerance relations and operator systems ⋮ The relative Mishchenko-Fomenko higher index and almost flat bundles. II: Almost flat index pairing ⋮ Controlled \(K\)-theory for groupoids \& applications to coarse geometry ⋮ Higher \(\rho\) invariant is an obstruction to the inverse being local ⋮ Quantitative \(K\)-theory for Banach algebras ⋮ Groupoids decomposition, propagation and operator \(K\)-theory ⋮ Decay of scalar curvature on uniformly contractible manifolds with finite asymptotic dimension ⋮ Low‐dimensional properties of uniform Roe algebras ⋮ Approximate ideal structures and \(K\)-theory ⋮ Higher invariants in noncommutative geometry ⋮ Dynamical complexity and K-theory of Lp operator crossed products ⋮ Persistence approximation property for maximal Roe algebras ⋮ The Novikov conjecture ⋮ Quantitative \(K\)-theory and the Künneth formula for operator algebras ⋮ \(L^p\) coarse Baum-Connes conjecture and \(K\)-theory for \(L^p\) Roe algebras ⋮ Going-down functors and the Künneth formula for crossed products by étale groupoids ⋮ Higher localised \(\hat{A}\)-genera for proper actions and applications

Cites Work

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• K-theory for the maximal Roe algebra of certain expanders
• The longitudinal index theorem for foliations
• Equivariant KK-theory and the Novikov conjecture
• The Novikov conjecture for groups with finite asymptotic dimension
• The Baum-Connes conjecture for amenable foliations
• Bivariant \(K\)-theory for Banach algebras and the Baum-Connes conjecture
• The coarse Baum-Connes conjecture and groupoids
• Cyclic cohomology, the Novikov conjecture and hyperbolic groups
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• K-theoretic amenability for \(SL_ 2({\mathbb{Q}}_ p)\), and the action on the associated tree
• A coarse Mayer–Vietoris principle
• Geometrization of the Strong Novikov Conjecture for residually finite groups
• Homotopy invariance of higher signatures and $3$-manifold groups
• K-theoretic amenability for discrete groups.
• Coarse cohomology and index theory on complete Riemannian manifolds
• \(E\)-theory and \(KK\)-theory for groups which act properly and isometrically on Hilbert space

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