# A product of trees as universal space for hyperbolic groups

@article{Buyalo2005APO, title={A product of trees as universal space for hyperbolic groups}, author={Sergei Buyalo and Viktor Schroeder}, journal={arXiv: Group Theory}, year={2005} }

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 .

## 8 Citations

Nagata dimension and quasi-Möbius maps

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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.

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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…

NAGATA DIMENSION AND QUASI-MÖBIUS MAPS

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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).

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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

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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

- Mathematics, Computer Science2013 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

- Computer Science, Mathematics2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)
- 2006

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).

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© 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…