Rigidity of secondary characteristic classes

✍ Scribed by Jerry M. Lodder

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 84 KB
• Volume: 12
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(00)00012-7

✦ Synopsis

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.