Fat minors in finitely presented groups

TL;DR

This paper establishes a characterization of finitely presented groups that virtually admit planar Cayley graphs, linking this property to being asymptotically minor-excluded, thus advancing understanding in geometric group theory.

Contribution

It proves that finitely presented groups have planar Cayley graphs virtually if and only if they are asymptotically minor-excluded, confirming a conjecture by Georgakopoulos and Papasoglu.

Findings

Finitely presented groups with planar Cayley graphs are characterized.

The paper confirms the conjecture relating planarity and minor-exclusion.

Provides a new criterion for understanding the geometry of finitely presented groups.

Abstract

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 Georgakopoulos and Papasoglu in the affirmative.