Amenable groups with very poor compression into Lebesgue spaces

DOI10.1215/00127094-1415860zbMath1226.43001arXiv0909.2047OpenAlexW1986778197MaRDI QIDQ638789

Tim D. Austin

Publication date: 14 September 2011

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.2047

zbMATH Keywords

amenable groupLipschitz embeddingCompression exponent

Mathematics Subject Classification ID

Geometric group theory (20F65) Metric geometry (51F99) Extensions, wreath products, and other compositions of groups (20E22) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (14)

Exotic crossed products and the Baum-Connes conjecture ⋮ A quasi-isometric embedding theorem for groups. ⋮ Stochastic approximation of lamplighter metrics ⋮ An introduction to the Ribe program ⋮ The Brin Prize works of Tim Austin ⋮ Speed of random walks, isoperimetry and compression of finitely generated groups ⋮ The Liouville property and Hilbertian compression ⋮ L ^p -distortion and p -spectral gap of finite graphs ⋮ \(L_p\) compression, traveling salesmen, and stable walks. ⋮ Quantitative nonlinear embeddings into Lebesgue sequence spaces ⋮ EQUIVARIANT COMPRESSION OF CERTAIN DIRECT LIMIT GROUPS AND AMALGAMATED FREE PRODUCTS ⋮ Group approximation in Cayley topology and coarse geometry Part I: Coarse embeddings of amenable groups ⋮ EMBEDDABILITY OF GENERALISED WREATH PRODUCTS ⋮ Metric behaviour of the Magnus embedding.

Cites Work

• Unnamed Item
• Unnamed Item
• \(L_p\) compression, traveling salesmen, and stable walks.
• Rectifiable sets and the traveling salesman problem
• Metrics on diagram groups and uniform embeddings in a Hilbert space.
• Quantitative property A, Poincaré inequalities, \(L^p\)-compression and \(L^p\)-distortion for metric measure spaces
• Uniform embeddings of metric spaces and of Banach spaces into Hilbert spaces
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• Isometric group actions on Hilbert spaces: growth of cocycles
• Proper actions of lamplighter groups associated with free groups
• Nonembeddability theorems via Fourier analysis
• Proper actions of wreath products and generalizations
• Embeddings of Discrete Groups and the Speed of Random Walks
• The wreath product of $\mathbb {Z}$ with $\mathbb {Z}$ has Hilbert compression exponent $\frac {2}{3}$
• COARSE EMBEDDINGS INTO A HILBERT SPACE, HAAGERUP PROPERTY AND POINCARÉ INEQUALITIES
• Compression functions of uniform embeddings of groups into Hilbert and Banach spaces
• EXACTNESS AND UNIFORM EMBEDDABILITY OF DISCRETE GROUPS
• Metric cotype

This page was built for publication: Amenable groups with very poor compression into Lebesgue spaces