Fat minors in finitely presented groups
Joseph MacManus

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.
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Taxonomy
TopicsRNA regulation and disease
