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math.GR2026
Almost planar finitely presented groups
John M. Mackay, Joseph P. MacManus, Davide Spriano
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 Georga…
math.GR2026
Realising all countable groups as quasi-isometry groups
Paula Heim, Joseph MacManus, Lawk Mineh
Given any countable group , we construct uncountably many quasi-isometry classes of proper geodesic metric spaces with quasi-isometry group isomorphic to . Moreover, if the g…
math.GR2024
Fat minors in finitely presented groups
Joseph MacManus
We show that a finitely presented group virtually admits a planar Cayley graph if and only if it is asymptotically minor-excluded, partially answering a conjecture of Georgakopoulo…