A bicombing that implies a sub-exponential isoperimetric inequality
Group Theory
2008-02-03 v1
Abstract
The idea of applying isoperimetric functions to group theory is due to M.Gromov. We introduce the concept of a ``bicombing of narrow shape'' which generalizes the usual notion of bicombing. Our bicombing is related to but different from the combings defined by M. Bridson. If the Cayley graph of a group with respect to a given set of generators admits a bicombing of narrow shape then the group is finitely presented and satisfies a sub-exponential isoperimetric inequality, as well as a polynomial isodiametric inequality. We give an infinite class of examples which are not bicombable in the usual sense but admit bicombings of narrow shape.
Cite
@article{arxiv.math/9310209,
title = {A bicombing that implies a sub-exponential isoperimetric inequality},
author = {Guenther Huck and Stephan Rosebrock},
journal= {arXiv preprint arXiv:math/9310209},
year = {2008}
}
Comments
LaTex, 10 pages, no figures