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arXiv · 2605.03040

Almost planar finitely presented groups

John M. Mackay·Joseph P. MacManus·Davide Spriano
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Abstract

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

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John M. Mackay, Joseph P. MacManus, Davide Spriano. 2026-05-04. Almost planar finitely presented groups. https://arxiv.org/abs/2605.03040

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