From the 1 of 4 linked papers with an AI index.
4 papers
Antipodal paths in covers of spheres
David Ellis, Maria-Romina Ivan, Imre Leader +1
The authors prove that if an n‑dimensional sphere is covered by k open sets with n ≥ 2k‑2, then one of the sets must contain a path whose endpoints are antipodal, and they show thi…
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…
Connecting conformal dimension and Poincaré profiles
David Hume, John M. Mackay
We strengthen the connection between the Ahlfors-regular (AR) conformal dimension Confdim of a compact AR metric space and a certain critical exponent of the Poincaré pro…
Property FA for random -gonal groups
Emily Clement, John M. Mackay
In the binomial -gonal model for random groups, where the random relations all have fixed length and the number of generators goes to infinity, we establish a do…