When does a right-angled Artin group split over $\mathbb{Z}$ ?

preprint2014arXivOpen access

We show that a right-angled Artin group, defined by a graph $Γ$ that has at least three vertices, does not split over an infinite cyclic subgroup if and only if $Γ$ is biconnected. Further, we compute JSJ--decompositions of 1--ended right-angled Artin groups over infinite cyclic subgroups.

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When does a right-angled Artin group split over $\mathbb{Z}$ ?

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When does a right-angled Artin group split over Z\mathbb{Z}Z?

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When does a right-angled Artin group split over $\mathbb{Z}$ ?