Geodesic
Diffeomorfism groups on noncompact manifolds
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–1, Tome 234 (1996), pp. 41-64

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A quite general theory of manifolds of maps between open manifolds of bounded geometry is constructed. The results of the paper can be applied to the case of compact manifolds, but the method used differs from the traditional approach of Ebin and Marsden. Bibl. 11 titles. 
@article{ZNSL_1996_234_a6,
     author = {J\"urgen Eichorn},
     title = {Diffeomorfism groups on noncompact manifolds},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {41--64},
     publisher = {mathdoc},
     volume = {234},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_234_a6/}
}
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Jürgen Eichorn. Diffeomorfism groups on noncompact manifolds. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part 15–1, Tome 234 (1996), pp. 41-64. http://geodesic.mathdoc.fr/item/ZNSL_1996_234_a6/