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arXiv · 2603.24706

Coarse separation and splittings in right-angled Artin groups

Oussama Bensaid·Anthony Genevois·Romain Tessera
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Abstract

In this article, we characterise geometrically when a right-angled Artin group splits over an abelian subgroup. More precisely, given a finite graph $\Gamma$, we show that $A(\Gamma)$ splits over an abelian subgroup if and only if it is coarsely separable by a family of subexponential growth, which amounts to saying that $\Gamma$ is complete or separated by a complete subgraph.

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Oussama Bensaid, Anthony Genevois, Romain Tessera. 2026-03-25. Coarse separation and splittings in right-angled Artin groups. https://arxiv.org/abs/2603.24706

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