John M. Mackay

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20232026

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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…