A bicombing that implies a sub-exponential isoperimetric inequality

Details A bicombing that implies a sub-exponential isoperimetric inequality A bicombing that implies a sub-exponential isoperimetric inequality

1993-10-23

arxiv.org/abs/math/9310209v1

Mathematics

Group Theory

LaTex, 10 pages, no figures

Scientific paper

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.

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