Operator algebra of foliations with projectively invariant transverse measure

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Yamashita, Makoto
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Abstract
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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.
Comment: 24 pages; thoroughly revised, to appear in Publ. RIMS
Keywords
Mathematics - Operator Algebras, Mathematics - K-Theory and Homology, 58B34, 46L87
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