Generalized Dehn Functions II
Group Theory
2009-01-16 v1 Geometric Topology
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.
Cite
@article{arxiv.0901.2317,
title = {Generalized Dehn Functions II},
author = {Chad Groft},
journal= {arXiv preprint arXiv:0901.2317},
year = {2009}
}
Comments
10 pages