6 papers
Minor exclusion and planar rigidity
Joseph Paul MacManus
We prove that every connected, locally finite, quasi-transitive graph which is quasi-isometric to a graph excluding a countable clique as a minor is quasi-isometric to a planar gra…
Relative accessibility for graphs
Joseph Paul MacManus
We relativise the Thomassen--Woess definition of accessibility in graphs, defining what it means for a graph to be accessible relative to a peripheral system. In the case of locall…
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…
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…
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…
Tiling in some nonpositively curved groups
Joseph MacManus, Lawk Mineh
We prove that acylindrically hyperbolic groups are monotileable. That is, every finite subset of the group is contained in a finite tile. This provides many new examples of monotil…