Rigidity of secondary characteristic classes
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 \(H_{dR}^4(M)\) is computed, where \(HL^*\) denotes Leibniz cohomology and \(H_{dR}^*\) denotes de Rham cohomology.
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