# The asymptotic dimension of box spaces of virtually nilpotent groups

## TL;DR

This paper proves that the asymptotic dimension of box spaces of virtually nilpotent groups equals the Hirsch length, providing a precise geometric invariant for these groups.

## Contribution

It establishes a direct link between the asymptotic dimension of box spaces and the Hirsch length for virtually nilpotent groups, a novel geometric characterization.

## Key findings

- Asymptotic dimension of box spaces equals Hirsch length
- Valid for all virtually nilpotent groups
- Provides a new geometric invariant

## Abstract

We show that every box space of a virtually nilpotent group has asymptotic dimension equal to the Hirsch length of that group.