Proper actions of wreath products and generalizations

DOI10.1090/S0002-9947-2012-05475-4zbMath1283.20049arXiv0905.3960MaRDI QIDQ2884399

Yves Stalder, Alain Valette, Yves De Cornulier

Publication date: 29 May 2012

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.3960

zbMATH Keywords

wreath productsHaagerup propertycoarse embeddingsKazhdan property Tmeasured walls

Mathematics Subject Classification ID

Geometric group theory (20F65) Extensions, wreath products, and other compositions of groups (20E22) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (34)

Infinite presentability of groups and condensation ⋮ Classification of Thompson related groups arising from Jones' technology II ⋮ Median sets of isometries in \(\mathrm{CAT}(0)\) cube complexes and some applications ⋮ Haagerup property and Kazhdan pairs via ergodic infinite measure preserving actions ⋮ A note on torsion subgroups of groups acting on finite-dimensional CAT(0) cube complexes ⋮ Lamplighter groups, median spaces and Hilbertian geometry ⋮ Group measure space decomposition of \(\text{II}_{1}\) factors and \(\text W^{*}\)-superrigidity ⋮ A non-trivial example of a free-by-free group with the Haagerup property. ⋮ Haagerup property for wreath products constructed with Thompson's groups ⋮ Coarse geometry of Hecke pairs and the Baum-Connes conjecture ⋮ Stochastic approximation of lamplighter metrics ⋮ No quasi-isometric rigidity for proper actions on CAT(0) cube complexes ⋮ Von Neumann equivalence and 𝑀_{𝑑} type approximation properties ⋮ Forest-skein groups II: Construction from homogeneously presented monoids ⋮ Topological actions of wreath products ⋮ \(\operatorname{SL}_2\) representations and relative property (T) ⋮ Amenable groups with very poor compression into Lebesgue spaces ⋮ A class of II\(_{1}\) factors with many non conjugate Cartan subalgebras ⋮ Speed of random walks, isoperimetry and compression of finitely generated groups ⋮ The Baum–Connes conjecture: an extended survey ⋮ \(L_p\) compression, traveling salesmen, and stable walks. ⋮ Compression bounds for wreath products ⋮ Haagerup approximation property for quantum reflection groups ⋮ A curiously cubulated group ⋮ On the bi-Lipschitz geometry of lamplighter graphs ⋮ EQUIVARIANT COMPRESSION OF CERTAIN DIRECT LIMIT GROUPS AND AMALGAMATED FREE PRODUCTS ⋮ LOCALLY COMPACT WREATH PRODUCTS ⋮ \(K\)-theory and \(K\)-homology of finite wreath products with free groups ⋮ On relative property (T) and Haagerup’s property ⋮ Maximal subgroups and von Neumann subalgebras with the Haagerup property ⋮ Random walks on the discrete affine group ⋮ EMBEDDABILITY OF GENERALISED WREATH PRODUCTS ⋮ Permanence properties of verbal products and verbal wreath products of groups ⋮ Relative expanders

Cites Work

• Metrics on diagram groups and uniform embeddings in a Hilbert space.
• Isometric group actions on Banach spaces and representations vanishing at infinity
• Kazhdan and Haagerup properties from the median viewpoint.
• The metrical interpretation of superreflexivity in Banach spaces
• Buildings of spherical type and finite BN-pairs
• Addendum to ``Random walk in random groups by M. Gromov.
• Proper actions of lamplighter groups associated with free groups
• Quasi-isometrically embedded free sub-semigroups.
• Relative property (T) and related properties of wreath products
• On relative property (T) and Haagerup’s property
• Relative Kazhdan Property
• Hecke algebras
• Compression bounds for wreath products
• The wreath product of $\mathbb {Z}$ with $\mathbb {Z}$ has Hilbert compression exponent $\frac {2}{3}$
• Growth Series of Some Wreath Products
• Negative definite kernels and a dynamical characterization of property (T) for countable groups
• Spaces with measured walls, the Haagerup property and property (T)
• Constructions preserving Hilbert space uniform embeddability of discrete groups
• Geometry of cuts and metrics
• \(E\)-theory and \(KK\)-theory for groups which act properly and isometrically on Hilbert space
• Groups with the Haagerup property. Gromov's a-T-menability
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