1993/10/23 by Guenther Huck, Huck, Guenther, Stephan Rosebrock +1
Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematics and Applications #Point processes and geometric inequalities #math.GR
paper · pdf · doi:10.48550/arxiv.math/9310209
LaTex, 10 pages, no figures
arxiv created 1993/10/23 · openalex publication_date 1993/10/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.