English

Almost planar finitely presented groups

Group Theory 2026-05-06 v1 Combinatorics Metric Geometry

Abstract

We show that finitely presented groups which admit kk-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 kk-planar, coarsely simply connected, connected, locally finite, quasi-transitive graph is quasi-isometric to a planar graph.

Keywords

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!

R2 v1 2026-07-01T12:49:17.141Z