Hyperbolically embedded subgroups and quasi-isometries of pairs

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.

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

References in corpus (1)

• Quasi-isometric rigidity of subgroups and Filtered ends

Cited by in corpus (2)

• Relative cohomological dimension of a relatively hyperbolic pair
• The quasi-isometry invariance of the Coset Intersection Complex