The quasi-isometry invariance of commensurizer subgroups

TL;DR

This paper proves that certain subgroup structures called commensurizers are preserved under quasi-isometries in specific finitely presented groups, with various applications discussed.

Contribution

It establishes the quasi-isometry invariance of commensurizers of two-ended subgroups with at least three coends in one-ended finitely presented groups.

Findings

Commensurizers are invariant under quasi-isometries.

Applications of invariance are explored.

Results contribute to understanding geometric group theory.

Abstract

We prove that commensurizers of two-ended subgroups with at least three coends in one-ended, finitely presented groups are invariant under quasi-isometries. We discuss a variety of applications of this result.