On quasi-isometric nilpotent Lie groups

TL;DR

This paper provides evidence supporting the conjecture that quasi-isometric simply-connected nilpotent Lie groups are isomorphic, by constructing examples demonstrating their rigidity under quasi-isometry.

Contribution

The authors construct new examples of simply-connected nilpotent Lie groups that are rigid, showing that quasi-isometry implies isomorphism in these cases.

Findings

Constructed examples of rigid nilpotent Lie groups

Evidence supporting the conjecture on quasi-isometric groups

Demonstrated that quasi-isometry implies isomorphism for these examples

Abstract

In this article we provide evidence for a well-known conjecture which states that quasi-isometric simply-connected nilpotent Lie groups are isomorphic. We do so by constructing new examples which are rigid in the sense that whenever they are quasi-isometric to any other simply-connected nilpotent Lie group, the groups are actually isomorphic.