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

Abstract

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

v2: fixed errors, improved exposition; v1: 14 pages

Cited by in corpus (2)

• JSJ decompositions of groups
• Embeddability and quasi-isometric classification of partially commutative groups