THE COARSE BAUM–CONNES CONJECTURE FOR RELATIVELY HYPERBOLIC GROUPS

DOI10.1142/S1793525312500021zbMath1251.58008arXiv1109.6377WikidataQ123265898 ScholiaQ123265898MaRDI QIDQ2885382

Tomohiro Fukaya, Shin-ichi Oguni

Publication date: 23 May 2012

Published in: Journal of Topology and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.6377

zbMATH Keywords

coarse geometryNovikov conjectureBaum-Connes conjecturerelatively hyperbolic group

Mathematics Subject Classification ID

Geometric group theory (20F65) (K)-theory and operator algebras (including cyclic theory) (46L80) Exotic index theories on manifolds (58J22) Hyperbolic groups and nonpositively curved groups (20F67)

Related Items (9)

Expanders are counterexamples to the \(\ell^p\) coarse Baum-Connes conjecture ⋮ The coarse Baum-Connes conjecture for certain relative expanders ⋮ The equivariant coarse Baum-Connes conjecture for metric spaces with proper group actions ⋮ A coarse Cartan–Hadamard theorem with application to the coarse Baum–Connes conjecture ⋮ The equivariant coarse Novikov conjecture and coarse embedding ⋮ Extending properties to relatively hyperbolic groups ⋮ Coarse embedding into uniformly convex Banach spaces ⋮ Coronae of relatively hyperbolic groups and coarse cohomologies ⋮ Coronae of product spaces and the coarse Baum-Connes conjecture

Cites Work

• Representable K-theory for \(\sigma\)-C\({}^*\)-algebras
• Relative hyperbolicity and relative quasiconvexity for countable groups.
• Dehn filling in relatively hyperbolic groups.
• The Novikov conjecture for groups with finite asymptotic dimension
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• Boundary amenability of relatively hyperbolic groups.
• A coarse Mayer–Vietoris principle
• Classifying Spaces and Boundaries for Relatively Hyperbolic Groups
• Coarse homology theories

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