Higher divergence for nilpotent groups

TL;DR

This paper investigates the higher divergence in nilpotent Lie groups, showing that additional filling requirements do not significantly affect their isoperimetric behavior, and computes this divergence for Heisenberg groups across all dimensions.

Contribution

It demonstrates that higher divergence behaves similarly to higher-dimensional Dehn functions in many nilpotent Lie groups, including explicit results for Heisenberg groups.

Findings

Higher divergence aligns with higher-dimensional Dehn functions in many nilpotent groups.

The higher divergence of Heisenberg groups is computed in all dimensions.

Additional filling requirements do not significantly alter divergence in these groups.

Abstract

The higher divergence of a metric space describes its isoperimetric behaviour at infinity. It is closely related to the higher-dimensional Dehn functions, but has more requirements to the fillings. We prove that these additional requirements do not have an essential impact for many nilpotent Lie groups. As a corollary, we obtain the higher divergence of the Heisenberg groups in all dimensions.