English

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.

Keywords

Cite

@article{arxiv.0901.2317,
  title  = {Generalized Dehn Functions II},
  author = {Chad Groft},
  journal= {arXiv preprint arXiv:0901.2317},
  year   = {2009}
}

Comments

10 pages

R2 v1 2026-06-21T12:01:23.443Z