Almost planar finitely presented groups
Group Theory
2026-05-06 v1 Combinatorics
Metric Geometry
Abstract
We show that finitely presented groups which admit -planar Cayley graphs contain finite-index subgroups with planar Cayley graphs. More generally, we answer a question of Georgakopoulos and Papasoglu in the special case of coarsely simply connected graphs: a -planar, coarsely simply connected, connected, locally finite, quasi-transitive graph is quasi-isometric to a planar graph.
Cite
@article{arxiv.2605.03040,
title = {Almost planar finitely presented groups},
author = {John M. Mackay and Joseph P. MacManus and Davide Spriano},
journal= {arXiv preprint arXiv:2605.03040},
year = {2026}
}
Comments
26 pages, 4 figures. Comments welcome!