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Diffeomorphism groups on noncompact manifolds. (English. Russian original) Zbl 0930.58007

J. Math. Sci., New York 94, No. 2, 1162-1176 (1999); translation from Zap. Nauchn. Semin. POMI 234, 41-65 (1996).
This paper outlines a theory of manifolds of maps between open manifolds of bounded geometry. It relies heavily on a seven-year-old preprint of the author, and about half of the paper is devoted to summarizing relevant results from that paper. The climax is the fitting of the space of maps into the context of ILH-Lie groups. For example, \(\{ D^{2,\infty}_0,D^{2,r}_0\;/\;r\geq n/2+1\}\) is an ILH-Lie group, where \(D^{2,\infty}_0=\lim_{\leftarrow}D^{2,r}_0\) and \(D^{2,r}_0\) is the identity component of a space of maps of an oriented, open, complete Riemannian manifold satisfying some boundedness conditions.
It is noted in passing that the theorem on page 1165 is false in the full generality in which it is stated but is valid in the context in which it is applied.

MSC:

58D15 Manifolds of mappings
58D05 Groups of diffeomorphisms and homeomorphisms as manifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
54E15 Uniform structures and generalizations

Citations:

Zbl 0924.00014
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References:

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