Approximate groups, I: the torsion-free nilpotent case

TL;DR

This paper investigates the structure of approximate subgroups within torsion-free nilpotent groups, emphasizing Lie groups, and discusses related recent research in the field.

Contribution

It provides a detailed structural description of K-approximate subgroups in torsion-free nilpotent groups, connecting with recent independent works.

Findings

Characterization of approximate subgroups in torsion-free nilpotent groups

Connections between different recent approaches in the field

Insights into the structure of approximate subgroups in Lie groups

Abstract

We describe the structure of ``K-approximate subgroups'' of torsion-free nilpotent groups, paying particular attention to Lie groups. Three other works, by Fisher-Katz-Peng, Sanders and Tao, have appeared which independently address related issues. We comment briefly on some of the connections between these papers.