Characterization of the Haagerup property by fibred coarse embedding into Hilbert space

DOI10.1112/BLMS/BDT045zbMath1347.20043OpenAlexW2100284855MaRDI QIDQ2854238

Xiaoman Chen, Qin Wang, Xian-Jin Wang

Publication date: 18 October 2013

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/blms/bdt045

zbMATH Keywords

finitely generated residually finite groupscoarse Baum-Connes conjectureHaagerup propertybox spacesfibred coarse embeddings into Hilbert spaces

Mathematics Subject Classification ID

Geometric group theory (20F65) Noncommutative differential geometry (46L87) (K)-theory and operator algebras (including cyclic theory) (46L80) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Residual properties and generalizations; residually finite groups (20E26) Index theory (19K56) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85)

Related Items (19)

Expanders and box spaces ⋮ Fibred cofinitely-coarse embeddability of box families and proper isometric affine actions on uniformly convex Banach spaces ⋮ Uniformly bounded fibred coarse embeddability and uniformly bounded a-T-menability ⋮ From the geometry of box spaces to the geometry and measured couplings of groups ⋮ The coarse Baum-Connes conjecture for certain relative expanders ⋮ A Bott periodicity theorem for \(\ell^p\)-spaces and the coarse Novikov conjecture at infinity ⋮ Characterization of the Haagerup property for residually amenable groups ⋮ 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 ⋮ Sofic boundaries of groups and coarse geometry of sofic approximations ⋮ Box spaces of the free group that neither contain expanders nor embed into a Hilbert space ⋮ Persistence approximation property for maximal Roe algebras ⋮ Coarse fundamental groups and box spaces ⋮ Group approximation in Cayley topology and coarse geometry Part I: Coarse embeddings of amenable groups ⋮ Group approximation in Cayley topology and coarse geometry. II: Fibred coarse embeddings ⋮ Relative expanders ⋮ Group approximation in Cayley topology and coarse geometry. III: Geometric property (T)

This page was built for publication: Characterization of the Haagerup property by fibred coarse embedding into Hilbert space