Quasi-isometry classification of right-angled Artin groups that split over cyclic subgroups

  • Alexander Margolis

    Vanderbilt University, Nashville, USA
Quasi-isometry classification of right-angled Artin groups that split over cyclic subgroups cover

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Abstract

For a one-ended right-angled Artin group, we give an explicit description of its JSJ tree of cylinders over infinite cyclic subgroups in terms of its defining graph. This is then used to classify certain right-angled Artin groups up to quasi-isometry. In particular, we show that if two right-angled Artin groups are quasi-isometric, then their JSJ trees of cylinders are weakly equivalent. Although the converse to this is not generally true, we define quasi-isometry invariants known as stretch factors that can distinguish quasi-isometry classes of RAAGs with weakly equivalence JSJ trees of cylinders. We then show that for many right-angled Artin groups, being weakly equivalent and having matching stretch factors is a complete quasi-isometry invariant.

Cite this article

Alexander Margolis, Quasi-isometry classification of right-angled Artin groups that split over cyclic subgroups. Groups Geom. Dyn. 14 (2020), no. 4, pp. 1351–1417

DOI 10.4171/GGD/584