Coarse separation and splittings in right-angled Artin groups

Abstract

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

36 pages, 14 figures. Comments are welcome!