We bound the higher-order Dehn functions and other filling invariants of certain Carnot groups using approximation techniques. These groups include the higher-dimensional Heisenberg groups, jet groups, and central products of 2-step nilpotent groups. Some consequences of this work are a construction of groups with arbitrarily large nilpotency class that have Euclidean n-dimensional filling volume functions, and a proof of part of a conjecture of Gromov on the higher-order filling functions of the higher-dimensional Heisenberg groups.
Cite this article
Robert Young, Filling inequalities for nilpotent groups through approximations. Groups Geom. Dyn. 7 (2013), no. 4, pp. 977–1011DOI 10.4171/GGD/213