Generalized Dehn Functions II

Details Generalized Dehn Functions II Generalized Dehn Functions II

2009-01-15

arxiv.org/abs/0901.2317v1

Mathematics

Group Theory

10 pages

Scientific paper

We establish the existence, finiteness, and uniqueness up to scaling of various isoperimetric profiles of a group, in all dimensions. We also show that these profiles all coincide in dimensions 4 and higher; in particular, the nth Dehn function is equal to FV^{n+1} for n at least 3. Even for dimension 3, there is significant overlap. When a group has decidable word problem, this has mild consequences for the growth rates of its profiles. We also establish a metric analogue for highly connected Riemannian manifolds.

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