Free minimal actions of solvable Lie groups which are not affable

TL;DR

This paper constructs a large family of complex group actions on compact spaces that are minimal and free but do not exhibit affability or quasi-isometric orbit properties, expanding understanding of group dynamics.

Contribution

It introduces uncountably many examples of solvable group actions with unique dynamical properties not previously documented.

Findings

Existence of uncountably many non-affable, free minimal actions

Orbits are not quasi-isometric to Cayley graphs

Construction of transversely Cantor laminations

Abstract

We construct an uncountable family of transversely Cantor laminations of compact spaces defined by free minimal actions of solvable groups, which are not affable and whose orbits are not quasi-isometric to Cayley graphs.