Averaged Dehn functions for nilpotent groups

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• 作者：Robert Young
• 关键词：Dehn functions ; Random walks ; Nilpotent groups
• 刊名：Topology
• 出版年：2008
• 期刊代码：59_00409383
• 类别：mt
• 出版时间：September 2008
• 卷：47
• 期：5
• 页码：351-367
• 文件大小：340 K

摘要

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 for >2, then it satisfies the averaged isoperimetric inequality . In the case of non-abelian free nilpotent groups, the bounds we give are asymptotically sharp.