Averaged Dehn Functions for Nilpotent Groups

2005/10/31 by Robert Young, Young, Robert
Mathematics · #20F18 #20F65 (Primary) #60G50 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20F18 #msc:20F65 #msc:60G50

paper · pdf · doi:10.48550/arxiv.math/0510665

15 pages, 1 figure; many corrections/clarifications, expanded proof of main theorem, added Proposition 4. To appear in Topology

arxiv created 2007/09/20 · arxiv updated 2009/12/01

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)<Cl^α for α>2 then it satisfies the averaged isoperimetric inequality δ^avg(l)<C'l^α/2. In the case of non-abelian free nilpotent groups, the bounds we give are asymptotically sharp.

Related

• Random Dehn function of groups
• Tracking rates of random walks
• Generalized Dehn Functions II
• Small-ball estimates for random walks on groups
• Nilpotent groups without exactly polynomial Dehn function