Filling inequalities for nilpotent groups through approximations

Research output: Contribution to journalArticlepeer-review

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 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.

Original languageEnglish (US)
Pages (from-to)977-1011
Number of pages35
JournalGroups, Geometry, and Dynamics
Volume7
Issue number4
DOIs
StatePublished - 2013

Keywords

  • Dehn function
  • Filling inequalities
  • Heisenberg group
  • Nilpotent groups

ASJC Scopus subject areas

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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