Higher divergence for nilpotent 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.

14 pages, 4 figures