JournalsjncgVol. 4 , No. 3DOI 10.4171/jncg/60

Le coût est un invariant isopérimétrique

  • Mikaël Pichot

    IPMU, Tokyo
  • Stéphane Vassout

    Institut de Mathématiques de Jussieu, Paris
Le coût est un invariant isopérimétrique cover

Abstract

Let RR be an ergodic measured equivalence relation of type II1 on a probability space (X,μ)(X, \mu) without atom. We show that

C(R)=1+12h(R)C(R)=1+\frac{1}{2}h(R)

where C(R)C(R) is the cost of RR, assumed to be finite, and h(R)h(R) its isoperimetric constant. This is a continuation of recent work of Russell Lyons and the authors on the subject.