Quasi-isometric classification of non-geometric 3-manifold groups

TL;DR

This paper classifies the quasi-isometry types of fundamental groups of most non-geometric 3-manifolds, completing a major part of the geometric group theory classification for 3-manifold groups.

Contribution

It provides a comprehensive quasi-isometric classification of non-geometric 3-manifold groups, covering cases with limited arithmetic hyperbolic components.

Findings

Complete quasi-isometric classification for most non-geometric 3-manifold groups.

Identification of conditions excluding certain arithmetic hyperbolic cases.

Extension of classification to all but a few exceptional cases.

Abstract

We describe the quasi-isometric classification of fundamental groups of irreducible non-geometric 3-manifolds which do not have "too many" arithmetic hyperbolic geometric components, thus completing the quasi-isometric classification of 3--manifold groups in all but a few exceptional cases.