Abstract
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 HL 4( g) to H ∗ dR (M) is computed, where HL ∗ denotes Leibniz cohomology and H ∗ dR denotes de Rham cohomology.
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