• Corpus ID: 18149781

A product of trees as universal space for hyperbolic groups

  title={A product of trees as universal space for hyperbolic groups},
  author={Sergei Buyalo and Viktor Schroeder},
  journal={arXiv: Group Theory},
We show that every Gromov hyperbolic group admits a quasiisometric embedding into the product of (n + 1) binary trees, where n = dim ∂1 is the topological dimension of the boundary at infinity of . 

Figures from this paper

On exactness and isoperimetric profiles of discrete groups
Nagata dimension and quasi-Möbius maps
We show that quasimobius maps preserve the Nagata dimension of metric spaces, generalizing a result of U. Lang and T. Schlichenmaier ([LS]). Mathematics Subject Classification (2000). 54F45, 30C65.
The asymptotic dimension of a curve graph is finite
We find an upper bound for the asymptotic dimension of a hyperbolic metric space with a set of geodesics satisfying a certain boundedness condition studied by Bowditch. The primary example is a
We show that quasi-Möbius maps preserve the Nagata dimension of metric spaces, generalizing a result of U. Lang and T. Schlichenmaier (Int. Math. Res. Not. 2005, no. 58, 3625–3655).
Asymptotic dimension and uniform embeddings
We show that the type function of a space with finite asymptotic dimension estimates its Hilbert (or any $l^p$) compression. The method allows to obtain the lower bound of the compression of the
Asymptotic isoperimetry on groups and uniform embeddings into Banach spaces
We characterize the possible asymptotic behaviors of the compression associated to a uniform embedding into some Lp-space, with 1 < p < ∞, for a large class of groups including connected Lie groups
Non-positive Curvature and the Planar Embedding Conjecture
  • Anastasios Sidiropoulos
  • Mathematics, Computer Science
    2013 IEEE 54th Annual Symposium on Foundations of Computer Science
  • 2013
It is shown that every planar metric of non-positive curvature admits a constant-distortion embedding into L1, which confirms the planar embedding conjecture for the case ofnon-positively curved metrics.
Algorithms on negatively curved spaces
This work gives efficient algorithms and data structures for problems like approximate nearest-neighbor search and compact, low-stretch routing on subsets of negatively curved spaces of fixed dimension (including Hd as a special case).


Capacity dimension and embedding of hyperbolic spaces into a product of trees
We prove that every visual Gromov hyperbolic space X whose boundary at infinity has the finite capacity dimension n admits a quasi-isometric embedding into (n+1)-fold product of metric trees.
Embedding of hyperbolic Coxeter groups into products of binary trees and aperiodic tilings
We prove that a finitely generated, right-angled, hyperbolic Coxeter group can be quasiisometrically embedded into the product of n binary trees, where n is the chromatic number of . As application
Embeddings of Gromov Hyperbolic Spaces
It is shown that a Gromov hyperbolic geodesic metric space X with bounded growth at some scale is roughly quasi-isometric to a convex subset of hyperbolic space. If one is allowed to rescale the
Embedding of Hyperbolic Spaces in the Product of Trees
AbstractWe show that for each n ≥ 2 there is a quasi-isometric embedding of the hyperbolic space Hn in the product Tn=T × ··· × T of n copies of a (simplicial) metric tree T. On the other hand, we
The lp-Cohomology and the Conformal Dimension of Hyperbolic Cones
For any compact set K⊂RN we construct a hyperbolic graph CK, such that the conformal dimension of CK is at most the box dimension of K.
Homogeneous trees are bilipschitz equivalent
We prove that any two locally finite homogeneous trees with valency greater than 3 are bilipschitz equivalent. This implies that the quotienth1(G)/hk(G), wherehk (G) is thekthL2-Betti number ofG, is
Hyperbolic dimension of metric spaces
We introduce a new quasi-isometry invariant of metric spaces called the hyperbolic dimension, hypdim, which is a version of the Gromov's asymptotic dimension, asdim. The hyperbolic dimension is at
Recurrent geodesics on a surface of negative curvature
The results necessary for the development of this paper are contained in a paper by G. D. Birkhoff,t in a paper by J. Hadamard.J and in an earlier paper by the present writer. § In this earlier
Plongements lipschitziens dans Rn
A Lipschitz embedding of a mctric space (X, d) into another one (Y, 8) is an application / : X -»• Y such that : 3/1. B 6 ]0, + oo [. Vx. x ' e X, Ad(x, x ' ) 6(/(x), f{x'}) Bd(x, x'). We dcscribe
Au bord de certains polyèdres hyperboliques
© Annales de l’institut Fourier, 1995, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions