Finiteness properties and quasi-isometry of group pairs

TL;DR

This paper demonstrates that certain geometric and homological finiteness properties of group pairs remain invariant under a specific notion of quasi-isometry, advancing understanding of their geometric group theory.

Contribution

It introduces a notion of quasi-isometry for group pairs and proves the invariance of finiteness properties under this relation.

Findings

Finiteness properties are invariant under the new quasi-isometry.

Provides a framework for comparing group pairs geometrically.

Enhances understanding of geometric invariants in group theory.

Abstract

We show that the geometric and homological finiteness properties of group pairs are invariant under a suitable notion of quasi-isometry for group pairs.