English

On the boundary criterion for relative cubulation: multi-ended parabolics

Group Theory 2024-09-24 v1 Geometric Topology

Abstract

In this note, we clarify that the boundary criterion for relative cubulation of the first author and Groves works even when the peripheral subgroups are not one-ended. Specifically, if the boundary criterion is satisfied for a relatively hyperbolic group, we show that, up to taking a refined peripheral structure, the group admits a relatively geometric action on a CAT(0) cube complex. We anticipate that this refinement will be useful for constructing new relative cubulations in a variety of settings.

Keywords

Cite

@article{arxiv.2409.14290,
  title  = {On the boundary criterion for relative cubulation: multi-ended parabolics},
  author = {Eduard Einstein and Suraj Krishna MS and Thomas Ng},
  journal= {arXiv preprint arXiv:2409.14290},
  year   = {2024}
}

Comments

12 pages

R2 v1 2026-06-28T18:52:37.862Z