Geodesic
Finite-dimensional Lie algebras of formal vector fields and characteristic classes of homogeneous foliations
Izvestiya. Mathematics, Tome 10 (1976) no. 1, pp. 55-62 
D. B. Fuchs. Finite-dimensional Lie algebras of formal vector fields and characteristic classes of homogeneous foliations. Izvestiya. Mathematics, Tome 10 (1976) no. 1, pp. 55-62. http://geodesic.mathdoc.fr/item/IM2_1976_10_1_a3/
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     title = {Finite-dimensional {Lie} algebras of formal vector fields and characteristic classes of homogeneous foliations},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In [5], I. M. Gel'fand and the author computed the cohomology of the Lie algebra $W_n$ of formal vector fields in $n$-dimensional space. The present article is devoted to the study of homomorphisms $H^*(W_n;\mathbf R)\to H^*(\mathfrak g;\mathbf R)$ induced by imbeddings of finite-dimensional subalgebras in $W_n$. We show that there exist elements of $H^*(W_n;\mathbf R)$ which are annihilated by any such homomorphism. On the other hand, we show that the image of the cohomology homomorphism induced by the well-known embedding $\mathfrak{sl}(n+1,\mathbf R)\to W_n$ has dimension $2^{n-1}+1$. The results are applied to characteristic classes of foliations. Bibliography: 9 titles.

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[2] Bott R., “Some remarks on continuous cohomology”, Manifolds–Tokyo 1973 (Proc. Internat. Conf., Tokyo), Univ. Tokyo Press, Tokyo, 1973, 161–170 | MR

[3] Bott R., Haefliger A., “On characteristic classes of $\Gamma$-foliations”, Bull. Amer. Math. Soc., 78:6 (1972), 1039–1044 | DOI | MR | Zbl

[4] Gelfand I. M., Feigin B. L., Fuks D. B., “Kogomologii algebry Li formalnykh vektornykh polei s koeffitsientami v sopryazhennom s nei prostranstve i variatsii kharakteristicheskikh klassov sloenii”, Funkts. analiz, 8:2 (1974), 13–29 | MR

[5] Gelfand I. M., Fuks D. B., “Kogomologii algebry Li formalnykh vektornykh polei”, Izv. AN SSSR. Ser. matem., 34 (1970), 322–337 | MR

[6] Godbillon C., Vey J., “Un invariant des feuilletages de codimension 1”, Compt. rend. Acad. Sci. (Paris), 273:2 (1971), A92–A95 | MR

[7] Thurston W., “Foliations and groups of diffeomorpfisms”, Bull. Amer. Math. Soc., 80:2 (1974), 304–307 | DOI | MR | Zbl

[8] Fuks D. B., “O kharakteristicheskikh klassakh sloenii”, Uspekhi matem. nauk, 28:2 (1973), 3–17 | MR | Zbl

[9] Heitsch J., “On deformation of secondary characteristic classes”, Topology, 12:4 (1973), 381–388 | DOI | MR | Zbl