Coarse differentiation of quasi-isometries II: Rigidity for Sol and Lamplighter groups

TL;DR

This paper completes the proof of quasi-isometric rigidity for Sol and lamplighter groups, advancing understanding of their geometric and algebraic structures in the context of coarse differentiation.

Contribution

It provides the final steps in establishing the quasi-isometric rigidity of Sol and lamplighter groups, building on previous work and confirming their geometric uniqueness.

Findings

Proves quasi-isometric rigidity for Sol groups

Establishes quasi-isometric rigidity for lamplighter groups

Completes the proof initiated in prior work

Abstract

In this paper, which is the continuation of [EFW2], we complete the proof of the quasi-isometric rigidity of Sol and the lamplighter groups. The results were announced in [EFW1].