Coarse non-amenability and coarse embeddings

DOI10.1007/s00039-012-0145-zzbMath1275.46013arXiv1101.1993OpenAlexW2963218828MaRDI QIDQ412041

Ján Špakula, Erik Guentner, Goulnara N. Arzhantseva

Publication date: 3 May 2012

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.1993

Mathematics Subject Classification ID

Geometric group theory (20F65) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Asymptotic properties of groups (20F69) Means on groups, semigroups, etc.; amenable groups (43A07) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85)

Related Items (26)

The Haagerup property for twisted groupoid dynamical systems ⋮ Boundary amenability of $Out(F_N)$ ⋮ From the geometry of box spaces to the geometry and measured couplings of groups ⋮ Uniform local amenability ⋮ Amenability and uniform Roe algebras ⋮ The coarse Baum-Connes conjecture for certain relative expanders ⋮ Low-distortion embeddings of graphs with large girth ⋮ Almost quasi-isometries and more non-C*-exact groups ⋮ Box spaces, group extensions and coarse embeddings into Hilbert space ⋮ A generalization of expander graphs and local reflexivity of uniform Roe algebras ⋮ Fibred coarse embeddings, a-T-menability and the coarse analogue of the Novikov conjecture ⋮ Embeddable box spaces of free groups ⋮ Ghostbusting and property A ⋮ The Baum–Connes conjecture: an extended survey ⋮ On the rigidity of uniform Roe algebras over uniformly locally finite coarse spaces ⋮ Sofic boundaries of groups and coarse geometry of sofic approximations ⋮ Group cubization ⋮ Coarse amenability versus paracompactness ⋮ Warped cones over profinite completions ⋮ Box spaces of the free group that neither contain expanders nor embed into a Hilbert space ⋮ A metric approach to limit operators ⋮ Embeddings of uniform Roe algebras ⋮ Group approximation in Cayley topology and coarse geometry Part I: Coarse embeddings of amenable groups ⋮ Logarithmic girth expander graphs of \(SL_n({\mathbb{F}}_p)\) ⋮ Straightening warped cones ⋮ Relative expanders

Cites Work

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• Groups acting on \(\text{CAT}(0)\) cube complexes
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• Coarsely embeddable metric spaces without Property A
• Amenable actions and exactness for discrete groups
• Maximal and reduced Roe algebras of coarsely embeddable spaces
• Amenable group actions and the Novikov conjecture
• Property A, partial translation structures, and uniform embeddings in groups
• Exactness and the Novikov conjecture

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