Additive quasi-isometries and cacti

Panos Papasoglu; Eric Swenson

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arXiv · 2609.15917

Additive quasi-isometries and cacti

Panos Papasoglu·Eric Swenson

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Abstract

We prove that if a geodesic metric space contains no $c$-fat theta curve for some $c>0$, then it is $(1,K)$-quasi-isometric to a cactus graph, where $K$ depends only on $c$. Using a coarse characterization of cacti in terms of $c$-fat theta curves this implies that every geodesic metric space quasi-isometric to a cactus is $(1,K)$-quasi-isometric to a cactus graph.

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BibTeX RIS

Panos Papasoglu, Eric Swenson. 2026-09-14. Additive quasi-isometries and cacti. https://arxiv.org/abs/2609.15917

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