Diffeological spaces

Authors

  • Martin Laubinger Louisiana State University.

DOI:

https://doi.org/10.4067/S0716-09172006000200003

Keywords:

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.

Author Biography

Martin Laubinger, Louisiana State University.

Mathematics Department.

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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[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).

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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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