English

Hyperbolically embedded subgroups and quasi-isometries of pairs

Group Theory 2025-01-15 v3

Abstract

We give technical conditions for a quasi-isometry of pairs to preserve a subgroup being hyperbolically embedded. We consider applications to the quasi-isometry and commensurability invariance of acylindrical hyperbolicity of finitely generated groups.

Keywords

Cite

@article{arxiv.2202.00536,
  title  = {Hyperbolically embedded subgroups and quasi-isometries of pairs},
  author = {Sam Hughes and Eduardo Martínez-Pedroza},
  journal= {arXiv preprint arXiv:2202.00536},
  year   = {2025}
}

Comments

Version 3. Added some discussion and open questions in new Section 6, to appear in Canadian Mathematical Bulletin, 18 pages. Version 2. Minor typos were corrected