Let be an ergodic measured equivalence relation of type II1 on a probability space without atom. We show that
where is the cost of , assumed to be finite, and its isoperimetric constant. This is a continuation of recent work of Russell Lyons and the authors on the subject.
Cite this article
Mikaël Pichot, Stéphane Vassout, Le coût est un invariant isopérimétrique. J. Noncommut. Geom. 4 (2010), no. 3, pp. 381–387DOI 10.4171/JNCG/60