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On the continuous cohomology of the Lie algebra of vector fields. (English) Zbl 0476.58032

MSC:
58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)
57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology
17B56 Cohomology of Lie (super)algebras
17B65 Infinite-dimensional Lie (super)algebras
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[1] I. M. Gel’fand and D. B. Fuks: Cohomology of Lie algebra of vector fields with non-trivial coefficients. Funkt. Anal. i Ego Pril., 4(3), 10-25 (1970). · Zbl 0222.58001 · doi:10.1007/BF01075238
[2] V. K. A. M. Gugenheim and J. P. May: On the theory and applications of differential torsion products. Memoirs of AMS, 142 (1974). · Zbl 0292.55019
[3] V. W. Guillemin: Cohomology of vector fields on a manifold. Advances in Math., 10, 192-220 (1973). · Zbl 0258.57012 · doi:10.1016/0001-8708(73)90108-4
[4] A. Haefliger: Sur la cohomologie de l’algebre de Lie des champs de vecteurs. Ann. scient. Ec. Norm. Sup., 4e serie, 9, 503-532 (1976). · Zbl 0342.57014 · numdam:ASENS_1976_4_9_4_503_0 · eudml:81985
[5] M. V. Losik: On the cohomologies of infinite-dimensional Lie algebras of vector fields. Funkt. Anal. i Ego Pril., 4(2), 43-53 (1970). · Zbl 0212.28002 · doi:10.1007/BF01094489
[6] M. V. Losik: Cohomologies of Lie algebras of vector fields with coefficients in a trivial unitary representation. Funkt. Anal. i Ego Pril., 6(1), 24-36 (1972). · Zbl 0299.58002 · doi:10.1007/BF01075506
[7] M. V. Losik: on cohomologies of Lie algebra of vector fields with non-trivial coefficients. Funkt. Anal. i Ego Pril., 6(4), 44-46 (1972). · Zbl 0284.17007 · doi:10.1007/BF01077647
[8] V. N. Reshetnikov: Cohomology of Lie algebras of vector fields on a manifold vanishing at a given point. Uspehi Mat. Nauk, 27(1), 251-252 (1972). · Zbl 0246.57020
[9] V. N. Reshetnikov: On the cohomology of the Lie algebras of vector fields on a manifold with non-trivial coefficients. Dokl. Akad. Nauk SSSR, 208(5), 234-240 (1973). · Zbl 0295.57009
[10] K. Shiga: Cohomology of Lie algebras over a manifold. I. J. Math. Soc. Japan, 26(2), 324-361 (1974). · Zbl 0273.58002 · doi:10.2969/jmsj/02620324
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