Averaged Dehn Functions for Nilpotent Groups

Details Averaged Dehn Functions for Nilpotent Groups Averaged Dehn Functions for Nilpotent Groups

2005-10-31

arxiv.org/abs/math/0510665v4

Mathematics

Group Theory

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

Scientific paper

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 $\delta(l)2$ then it satisfies the averaged isoperimetric inequality $\delta^{\text{avg}}(l)

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