Compression functions of uniform embeddings of groups into Hilbert and Banach spaces

DOI10.1515/CRELLE.2009.066zbMath1258.20032arXivmath/0612378OpenAlexW2151697178MaRDI QIDQ3647067

Cornelia Drutu, Goulnara N. Arzhantseva, Mark V. Sapir

Publication date: 27 November 2009

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612378

zbMATH Keywords

finitely generated groupsquasi-isometriesuniformly convex Banach spacesasymptotic dimensionHilbert space compressionuniform embeddability

Mathematics Subject Classification ID

Selfadjoint operator algebras ((C^*)-algebras, von Neumann ((W^*)-) algebras, etc.) (46L99) Geometric group theory (20F65) Asymptotic properties of groups (20F69) Groups acting on trees (20E08) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85)

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A quasi-isometric embedding theorem for groups., Stochastic approximation of lamplighter metrics, Assouad-Nagata dimension of connected Lie groups, An introduction to the Ribe program, Compression bounds for Lipschitz maps from the Heisenberg group to \(L_{1}\), On the dimension growth of groups., Distortion of imbeddings of groups of intermediate growth into metric spaces, Amenable groups with very poor compression into Lebesgue spaces, Hilbert space compression for free products and HNN-extensions., Speed of random walks, isoperimetry and compression of finitely generated groups, Log-Lipschitz embeddings of homogeneous sets with sharp logarithmic exponents and slicing products of balls, Asymptotic dimension and uniform embeddings., \(L_p\) compression, traveling salesmen, and stable walks., Quantitative nonlinear embeddings into Lebesgue sequence spaces, Group approximation in Cayley topology and coarse geometry Part I: Coarse embeddings of amenable groups

Cites Work

• Hilbert space compression and exactness of discrete groups.
• The coarse geometric Novikov conjecture and uniform convexity
• Two singular dynamics of the nonlinear Schrödinger equation on a plane domain
• The geometry of graphs and some of its algorithmic applications
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• Asymptotic dimension of discrete groups
• Expander graphs and their applications
• Uniform embeddings of bounded geometry spaces into reflexive Banach space
• On a formula for the asymptotic dimension of free products