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arXiv · 0910.3414

The Gelfand-Kalinin-Fuks class and characteristic classes of transversely symplectic foliations

D. Kotschick·S. Morita
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Abstract

In the early 1970's, Gelfand, Kalinin and Fuks found an exotic characteristic class of degree 7 in the Gelfand-Fuks cohomology of the Lie algebra of formal Hamiltonian vector fields on the plane. We prove that this cohomology class can be decomposed as a product of a certain leaf cohomology class of degree 5 and the transverse symplectic class. This is similar to the well known factorization of the Godbillon-Vey class for codimension n foliations. We also interpret the characteristic classes of transversely symplectic foliations introduced by Kontsevich in terms of the known classes and prove non-triviality for some of them.

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D. Kotschick, S. Morita. 2009-10-18. The Gelfand-Kalinin-Fuks class and characteristic classes of transversely symplectic foliations. https://arxiv.org/abs/0910.3414

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