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Additive quasi-isometries and cacti
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
@misc{papasoglu2026additive,
title = {{Additive quasi-isometries and cacti}},
author = {Panos Papasoglu and Eric Swenson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15917},
eprint = {2609.15917},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15917},
}
RIS
TY - UNPB
TI - Additive quasi-isometries and cacti
AU - Panos Papasoglu
AU - Eric Swenson
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15917
UR - https://arxiv.org/abs/2609.15917
AB - 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.
ER -