Filling inequalities for nilpotent groups

Abstract

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 two-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.

29 pages, 2 figures; entirely rewritten and merged with arXiv:math/0601297

References in corpus (3)

• Scaled relators and Dehn functions for nilpotent groups
• The asymptotic rank of metric spaces
• Averaged Dehn Functions for Nilpotent Groups

Cited by in corpus (6)

• Geometric presentations of Lie groups and their Dehn functions
• High-dimensional fillings in Heisenberg groups
• Homological and homotopical higher-order filling functions
• The Dehn function of Baumslag's Metabelian Group
• Contraction of areas vs. topology of mappings
• Contact equations, Lipschitz extensions and isoperimetric inequalities