Higher index theory for certain expanders and Gromov monster groups. II

DOI10.1016/j.aim.2011.12.016zbMath1243.46061arXiv1012.4151OpenAlexW2092736140MaRDI QIDQ664757

Rufus Willett, Guo-Liang Yu

Publication date: 2 March 2012

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

Full work available at URL: https://arxiv.org/abs/1012.4151

zbMATH Keywords

noncommutative geometryK-theoryhigher index theoryBaum-Connes conjectureexpandersRoe algebrasGromov's monster groups

Mathematics Subject Classification ID

Geometric group theory (20F65) Noncommutative topology (46L85) (K)-theory and operator algebras (including cyclic theory) (46L80) Index theory (19K56)

Related Items (21)

Uniformly bounded fibred coarse embeddability and uniformly bounded a-T-menability ⋮ The equivariant coarse Baum-Connes conjecture for spaces which admit an equivariant coarse embedding into Hilbert space ⋮ Expanders are counterexamples to the \(\ell^p\) coarse Baum-Connes conjecture ⋮ A Bott periodicity theorem for \(\ell^p\)-spaces and the coarse Novikov conjecture at infinity ⋮ The equivariant coarse Baum-Connes conjecture for metric spaces with proper group actions ⋮ The equivariant coarse Novikov conjecture and coarse embedding ⋮ Fibred coarse embeddings, a-T-menability and the coarse analogue of the Novikov conjecture ⋮ Embeddable box spaces of free groups ⋮ Fibred coarse embedding into non-positively curved manifolds and higher index problem ⋮ The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space ⋮ Higher invariants in noncommutative geometry ⋮ Higher index theory for certain expanders and Gromov monster groups. I ⋮ Geometric property (T) ⋮ Geometric property (T) for non-discrete spaces ⋮ Coarse fundamental groups and box spaces ⋮ The maximal injective crossed product ⋮ The coarse geometric \(\ell^p\)-Novikov conjecture for subspaces of nonpositively curved manifolds ⋮ The coarse Novikov conjecture and Banach spaces with property (H) ⋮ Random graphs, weak coarse embeddings, and higher index theory ⋮ Relative expanders ⋮ Group approximation in Cayley topology and coarse geometry. III: Geometric property (T)

Cites Work

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• Localization algebras and the coarse Baum-Connes conjecture
• Random walk in random groups.
• Property (T) and Kazhdan constants for discrete 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
• Deux remarques sur l'application de Baum–Connes
• A coarse Mayer–Vietoris principle
• Full Banach Mean Values on Countable groups.
• Geometrization of the Strong Novikov Conjecture for residually finite groups
• Aperiodic Tilings, Positive Scalar Curvature, and Amenability of Spaces
• Equivariant 𝐸-theory for 𝐶*-algebras
• \(E\)-theory and \(KK\)-theory for groups which act properly and isometrically on Hilbert space

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