Large Scale Geometry of Stratified Nilpotent Lie Groups

We develop a purely algebraic condition on the Lie algebra of a stratified nilpotent Lie group for having Euclidean filling functions in the low dimensions and sub-Euclidean filling functions in the high dimensions. We find a sufficient criterion for such groups to have a super-Euclidean filling function. Further we bound the higher divergence functions of stratified nilpotent Lie groups.