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A note on a paper of Palais

Author: L. Jonker
Journal: Proc. Amer. Math. Soc. 27 (1971), 337-340
MSC: Primary 53.45; Secondary 57.00
MathSciNet review: 0270288
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Abstract: If $ {\Phi ^p}$ denotes the space of smooth alternating $ p$-forms on the $ {C^\infty }$ manifold $ M$, we are interested in finding the spaces of $ R$-linear maps from $ {\Phi ^p}$ to $ {\Phi ^q}$ that commute with the diffeomorphisms of $ M$. For a compact manifold $ M$ these spaces were found by R. S. Palais. In this note we find them for noncompact $ M$.

References [Enhancements On Off] (What's this?)

  • [1] W. Greub and E. Stamm, On the multiplication of tensor fields, Proc. Amer. Math. Soc. 17 (1966) 1112-1119. MR 34 #729. MR 0200843 (34:729)
  • [2] L. Jonker, Natural differential operators, Ph.D. Thesis, University of Toronto, 1967.
  • [3] R. S. Palais, Natural operations on differential forms, Trans. Amer. Math. Soc. 92 (1959), 125-141. MR 22 #7140. MR 0116352 (22:7140)

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Keywords: Differential form, exterior derivative, integration of $ n$-forms, deRham cohomology
Article copyright: © Copyright 1971 American Mathematical Society

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