Diffeological spaces
DOI:
https://doi.org/10.4067/S0716-09172006000200003Keywords:
Differentiable Structures, differential geometry, differentiable spaces, estructuras diferenciales, geometría diferencial, espacios diferenciables.Abstract
We define diffeological spaces and give some examples. The diffeological category contains the category of smooth manifolds as full subcategory. We prove that diffeological spaces and smooth maps form a cartesian closed category. The concepts of differential form and tangent functor are extended from smooth manifolds to diffeological spaces.References
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[Frö86] A. Frölicher. Cartesian Closed Categories and Analysis of Smooth Maps, Volume 1174 : Categories in Continuum Physics of Lecture Notes in Mathematics, pp. 43-51, (1986).
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[Sou85] Jean Marie Souriau. Un algorithme générateur de structures quantiques. Astérisque, hors série, Societé Mathémarique de France, pp. 341-399, (1985).
[Don86] Paul Donato. Geometrie des Orbites Coadjointes des Groupes de Diffeomorphismes, volume 1416 : Geometrie Symplectique et Mecanique, Coloque International, La Grande Motte of Lecture Notes in Mathematics, pp. 84-104, Springer Verlag, (1988)
[Frö86] A. Frölicher. Cartesian Closed Categories and Analysis of Smooth Maps, Volume 1174 : Categories in Continuum Physics of Lecture Notes in Mathematics, pp. 43-51, (1986).
[Gio03] P. Giordano. Infinitesimal Differential Geometry, Pre-print arXiv:math. DG/0308119v2 17 Dec 2003, arXiv, (2003)
[Hec95] G. Hector. Géometrie et Topologie des Espaces Difféologiques, Analysis and Geometry in Foliated Manifolds, Proceedings of the VII International Colloquium on Differential Geometry, Santiago de Compostela, Spain, World Scientific, pp. 55-80, (1995).
[Mac71] Saunders Mc Lane. Categories for the Working Mathematician, Springer Verlag, New York, (1971).
[Sou85] Jean Marie Souriau. Un algorithme générateur de structures quantiques. Astérisque, hors série, Societé Mathémarique de France, pp. 341-399, (1985).
Published
2017-05-08
How to Cite
[1]
M. Laubinger, “Diffeological spaces”, Proyecciones (Antofagasta, On line), vol. 25, no. 2, pp. 151-178, May 2017.
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