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A Taxonomy of the Changing World of Design Practice: A vision of the changing role of design in society supported by a taxonomy matrix tool
Averaged Dehn Functions for Nilpotent Groups
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 then it satisfies the averaged
isoperimetric inequality . In the case
of non-abelian free nilpotent groups, the bounds we give are asymptotically
sharp.Comment: 15 pages, 1 figure; many corrections/clarifications, expanded proof
of main theorem, added Proposition 4. To appear in Topolog
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