Groups, Geometry, and Dynamics

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Volume 7, Issue 4, 2013, pp. 977–1011
DOI: 10.4171/GGD/213

Published online: 2013-11-20

Filling inequalities for nilpotent groups through approximations

Robert Young[1]

(1) University of Toronto, Canada

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.

Keywords: Dehn function, Heisenberg group, filling inequalities, nilpotent groups

Young Robert: Filling inequalities for nilpotent groups through approximations. Groups Geom. Dyn. 7 (2013), 977-1011. doi: 10.4171/GGD/213