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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Continuous cohomology for compactly supported vectorfields on $R^{n}$
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by Steven Shnider PDF
Trans. Amer. Math. Soc. 217 (1976), 364-377 Request permission

Abstract:

In this paper we study the Gelfand-Fuks cohomology of the Lie algebra of compactly supported vectorfields on ${{\mathbf {R}}^n}$ and establish the degeneracy of a certain spectral sequence at the ${E_1}$ level. We apply this result to the study of another spectral sequence introduced by Resetnikov for the cohomology of the algebra of vectorfields on ${S^n}$.
References
  • I. M. Gel′fand and D. B. Fuks, Cohomologies of the Lie algebra of tangent vector fields of a smooth manifold, Funkcional. Anal. i Priložen. 3 (1969), no. 3, 32–52 (Russian). MR 0256411
  • I. M. Gel′fand and D. B. Fuks, Cohomologies of the Lie algebra of tangent vector fields of a smooth manifold. II, Funkcional. Anal. i Priložen. 4 (1970), no. 2, 23–31 (Russian). MR 0285024
  • A. Kumpera and D. C. Spencer, Lie equations, Ann. of Math. Studies, Princeton Univ. Press, Princeton, N. J., 1973.
  • V. N. Rešetnikov, Cohomology with nontrivial coefficients of the Lie algebra of vector fields on a manifold, Dokl. Akad. Nauk SSSR 208 (1973), 1041–1043 (Russian). MR 0322870
  • Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, IX-X, Hermann, Paris, 1966 (French). Nouvelle édition, entiérement corrigée, refondue et augmentée. MR 0209834
  • S. Shnider, Notes on Gel’fand-Fuks cohomology, Available from Math. Dept, Princeton University, Princeton, N. J. P. Trauber, Continuous cohomology of the Lie algebra of vector fields, Thesis, Princeton University, Princeton, N. J., 1973. C. Godbillon, Cohomologie d’algèbres de Lie de champs de vecteurs formels, Séminaire Bourbaki 1972/73, Exposé 421.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 217 (1976), 364-377
  • MSC: Primary 57D30; Secondary 58H05, 57D25
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0418118-7
  • MathSciNet review: 0418118