LOSIK CLASSES FOR CODIMENSION-ONE FOLIATIONS

Abstract Following Losik’s approach to Gelfand’s formal geometry, certain characteristic classes for codimension-one foliations coming from the Gelfand-Fuchs cohomology are considered. Sufficient conditions nontriviality in terms of dynamical properties generators holonomy groups found. The Reeb is shown; this contrast with some classical theorems on Godbillon-Vey class; example, Mizutani-Morita-Tsuboi theorem about triviality class almost without not true under consideration. It shown that considered trivial a large holonomy. question related ergodic theory systems circle and problem smooth conjugacy local diffeomorphisms. Certain obstructions existence transverse affine projective connections.