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arXiv · 0901.2317

Generalized Dehn Functions II

Chad Groft
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Abstract

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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Chad Groft. 2009-01-15. Generalized Dehn Functions II. https://arxiv.org/abs/0901.2317

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