K-theory for the maximal Roe algebra of certain expanders

DOI10.1016/j.jfa.2009.04.017zbMath1185.46047arXiv0902.2317OpenAlexW2962987523MaRDI QIDQ1040577

Hervé Oyono-Oyono, Guo-Liang Yu

Publication date: 25 November 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.2317

zbMATH Keywords

coarse geometryNovikov conjectureBaum-Connes conjectureexpandersRoe algebrasoperator algebra K-theory

Mathematics Subject Classification ID

Geometric group theory (20F65) (K)-theory and operator algebras (including cyclic theory) (46L80) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Kasparov theory ((KK)-theory) (19K35) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85)

Related Items (23)

The coarse Novikov conjecture for coarse fibrations over Banach spaces with property (H) ⋮ Expanders are counterexamples to the \(\ell^p\) coarse Baum-Connes conjecture ⋮ The coarse Baum-Connes conjecture for certain relative expanders ⋮ Almost quasi-isometries and more non-C*-exact groups ⋮ A Bott periodicity theorem for \(\ell^p\)-spaces and the coarse Novikov conjecture at infinity ⋮ Codimension 2 transfer of higher index invariants ⋮ The equivariant coarse Baum-Connes conjecture for metric spaces with proper group actions ⋮ A Lichnerowicz vanishing theorem for the maximal Roe algebra ⋮ The equivariant coarse Novikov conjecture and coarse embedding ⋮ Fibred coarse embeddings, a-T-menability and the coarse analogue of the Novikov conjecture ⋮ Fibred coarse embedding into non-positively curved manifolds and higher index problem ⋮ Spaces of graphs, boundary groupoids and the coarse Baum-Connes conjecture ⋮ The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space ⋮ Higher index theory for certain expanders and Gromov monster groups. I ⋮ Higher index theory for certain expanders and Gromov monster groups. II ⋮ Geometric property (T) ⋮ The relative Mishchenko-Fomenko higher index and almost flat bundles. I: The relative Mishchenko-Fomenko index ⋮ Persistence approximation property for maximal Roe algebras ⋮ Coarse quotients by group actions and the maximal Roe algebra ⋮ On quantitative operator \(K\)-theory ⋮ A metric approach to limit operators ⋮ The coarse Novikov conjecture and Banach spaces with property (H) ⋮ Relative expanders

Cites Work

• Operator norm localization for linear groups and its application to \(K\)-theory
• Metric sparsification and operator norm localization
• The Baum-Connes conjecture for amenable foliations
• Discrete groups, expanding graphs and invariant measures. Appendix by Jonathan D. Rogawski
• Proper group actions and the Baum-Connes conjecture
• Baum-Connes conjecture and group actions on trees
• The coarse Baum-Connes conjecture and groupoids
• Counterexamples to the Baum-Connes conjecture
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• A coarse Mayer–Vietoris principle
• Geometrization of the Strong Novikov Conjecture for residually finite groups
• Coarse cohomology and index theory on complete Riemannian manifolds
• Permanence properties of the Baum-Connes conjecture
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