Higher dimensional isoperimetric functions in hyperbolic groups

Research output: Contribution to journalArticlepeer-review


We introduce the notion of an ℝ-combing and use it to show that hyperbolic groups satisfy linear isoperimetric inequalities for filling real cycles in each positive dimension. S. Gersten suggested the concept of metabolicity (over ℤ or ℝ) for groups which implies hyperbolicity. Metabolicity admits several equivalent definitions: by vanishing of ℓ-cohomology, using combings, and others. We prove several criteria for a group to be hyperbolic, ℝ-metabolicity being among them. In particular, a finitely presented group G is hyperbolic iff Hn(∞) (G, V) = 0 for any normed vector space V and any n ≥ 2.

Original languageEnglish (US)
Pages (from-to)327-345
Number of pages19
JournalMathematische Zeitschrift
Issue number2
StatePublished - Feb 2000
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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