A bicombing that implies a sub-exponential isoperimetric inequality

Günther Huck, S. R. Stephan Rosebrock

Research output: Contribution to journalArticle

Abstract

The idea of applying isoperimetric functions to group theory is due to M. Gromov [8], We introduce the concept of a “bicombing of narrow shape” which generalizes the usual notion of bicombing as defined for example in [5], [2], and [10]. Our bicombing is related to but different from the combings defined by M. Bridson [4]. If they 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.

Original languageEnglish (US)
Pages (from-to)515-523
Number of pages9
JournalProceedings of the Edinburgh Mathematical Society
Volume36
Issue number3
DOIs
StatePublished - 1993
Externally publishedYes

Keywords

  • 05C25
  • 1991 Mathematics subject classification
  • 20F05

ASJC Scopus subject areas

  • Mathematics(all)

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