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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Continuous cohomology for compactly supported vectorfields on $ R\sp{n}$


Author: Steven Shnider
Journal: Trans. Amer. Math. Soc. 217 (1976), 364-377
MSC: Primary 57D30; Secondary 58H05, 57D25
MathSciNet review: 0418118
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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}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0418118-7
PII: S 0002-9947(1976)0418118-7
Keywords: Continuous cohomology of a Lie algebra, Lie algebra of vectorfields, k jets of vectorfields, formal power series vectorfields, support of a distribution, degeneracy of a spectral sequence
Article copyright: © Copyright 1976 American Mathematical Society