Averaged Dehn functions for nilpotent groups

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Abstract

Gromov proposed an averaged version of the Dehn function and claimed that in many cases it should be subasymptotic to the Dehn function. Using results on random walks in nilpotent groups, we confirm this claim for most nilpotent groups. In particular, if a nilpotent group satisfies the isoperimetric inequality δ (l) < C lα for α > 2, then it satisfies the averaged isoperimetric inequality δavg (l) < C lα / 2. In the case of non-abelian free nilpotent groups, the bounds we give are asymptotically sharp.

Original languageEnglish (US)
Pages (from-to)351-367
Number of pages17
JournalTopology
Volume47
Issue number5
DOIs
StatePublished - Sep 2008

Keywords

  • Dehn functions
  • Nilpotent groups
  • Random walks

ASJC Scopus subject areas

  • Geometry and Topology

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