A product of trees as universal space for hyperbolic groups

TL;DR

This paper demonstrates that every Gromov hyperbolic group can be quasi-isometrically embedded into a product of binary trees, linking geometric group theory with tree structures based on boundary dimension.

Contribution

It introduces a universal embedding of hyperbolic groups into products of binary trees, extending understanding of their geometric structure.

Findings

Hyperbolic groups embed into products of binary trees

Embedding dimension relates to boundary topological dimension

Provides a universal geometric model for hyperbolic groups

Abstract

We show that every Gromov hyperbolic group $\Ga$ admits a quasi-isometric embedding into the product of $(n+1)$ binary trees, where $n=\dim\di\Ga$ is the topological dimension of the boundary at infinity of $\Ga$.