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A bicombing that implies a sub-exponential isoperimetric inequality

Guenther Huck·Stephan Rosebrock
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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.

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Guenther Huck, Stephan Rosebrock. 1993-10-23. A bicombing that implies a sub-exponential isoperimetric inequality. https://arxiv.org/abs/math/9310209

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