Rigidity of secondary characteristic classes

摘要

The topic of this paper is the rigidity of secondary characteristic classes associated to a flat connection on a differentiable manifold M. Viewing the connection as a Lie-algebra valued one-form for a Lie algebra g, it is proven that if the Leibniz cohomology of g vanishes, then all secondary characteristic classes for g are rigid. Moreover, in the case when g is the Lie algebra of formal vector fields and M supports a family of codimension one foliations, the image of a characteristic map from H L~4(g) to H_(dR)~* (M) is computed, where H L~* denotes Leibniz cohomology and H_(dR)~* denotes de Rham cohomology.