English

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

Group Theory 2014-08-04 v2

Abstract

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

Keywords

Cite

@article{arxiv.1403.1842,
  title  = {When does a right-angled Artin group split over $\mathbb{Z}$?},
  author = {Matt Clay},
  journal= {arXiv preprint arXiv:1403.1842},
  year   = {2014}
}

Comments

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

R2 v1 2026-06-22T03:22:31.848Z