John M. Mackay

collaborators

4 papers

math.AT2026

Antipodal paths in covers of spheres

David Ellis, Maria-Romina Ivan, Imre Leader +1

In this note we show that if the sphere $S^{n}$ is covered by $k$ open sets with $n \geq 2 k - 2$ , then one of these sets contains a path with antipodal endpoints. This is best…

math.GR2026

Almost planar finitely presented groups

John M. Mackay, Joseph P. MacManus, Davide Spriano

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 Georga…

math.GR2025

Connecting conformal dimension and Poincaré profiles

David Hume, John M. Mackay

We strengthen the connection between the Ahlfors-regular (AR) conformal dimension Confdim $(Z)$ of a compact AR metric space $Z$ and a certain critical exponent of the Poincaré prof…

math.GR2025

Property FA for random $ℓ$ -gonal groups

Emily Clement, John M. Mackay

In the binomial $ℓ$ -gonal model for random groups, where the random relations all have fixed length $ℓ \geq 3$ and the number of generators goes to infinity, we establish a do…

Antipodal paths in covers of spheres

Almost planar finitely presented groups

Connecting conformal dimension and Poincaré profiles

Property FA for random ℓ-gonal groups

Property FA for random $ℓ$ -gonal groups