Operator Algebra of Foliations with Projectively Invariant Transverse Measure

Abstract

We study the structure of operator algebras associated with the foliations which have projectively invariant measures. When a certain ergodicity condition on the measure preserving holonomies holds, the lack of holonomy invariant transverse measure can be established in terms of a cyclic cohomology class associated with the transverse fundamental cocycle and the modular automorphism group.