4 papers
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…