A product of trees as universal space for hyperbolic groups

Sergei Buyalo; Viktor Schroeder

A product of trees as universal space for hyperbolic groups

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arxiv math/0509355 v1 pith:CZZWQXNC submitted 2005-09-15 math.GR math.MG

Sergei Buyalo , Viktor Schroeder This is my paper · ORCID

classification math.GRmath.MG

keywords hyperbolicproducttreesadmitsbinaryboundarydimensionembedding

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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 $\Ga$.

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Near-Optimal Dynamic Steiner Spanners for Constant-Curvature Spaces
cs.CG 2025-09 conditional novelty 8.0 of 10

Near-optimal dynamic Steiner spanners are constructed in all three constant-curvature geometries via a quadtree approach, and the hyperbolic-plane 2-spanner problem is settled at Θ(n log n) edges.

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