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De Rham's theorem in a smooth topos

Published online by Cambridge University Press:  24 October 2008

Ieke Moerdijk  and
Gonzalo E. Reyes
Ieke Moerdijk
Affiliation:
Universiteit van Amsterdam
Gonzalo E. Reyes
Affiliation:
Université de Montréal
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Extract

It has been persuasively argued (e.g. by Lawvere[8]) that the mathematical world picture needed to develop the physics of continuous bodies and fields should involve a cartesian closed category of smooth morphisms between smooth spaces. As far as the foundations of the calculus of variations are concerned, the need for such a category was recognized by K. T. Chen(cf. [2]).

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 1 , July 1984 , pp. 61 - 71
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

[1] Bott, R. and Tu, L. W.. Differential Forms in Algebraic Topology, Graduate Texts in Math no. 83 (Springer-Verlag, 1982).CrossRefGoogle Scholar
[2] Chen, K.-T.. Iterated path integrals. ]Bull. Amer. Math. Soc. 83 (1977), 831–879.Google Scholar
[3] Dubuc, E. J.. [C∞-schemes.]Amer. J. Math. 103 (1981), 683–690.Google Scholar
[4] van Est, W. T.. A generalization of the Cartan-Leray spectral sequence. ]Indag. Math. 20 (1958), 399–413.CrossRefGoogle Scholar
[5] Glass, J. P.. De Rham cohomology with free parameters. To appear.Google Scholar
[6] Kock, A.. Synthetic Differential Geometry, L.M.S. Lectures Note series no. 51 (Cambridge University Press, 1981).Google Scholar
[7] Kock, A., Reyes, G. E. and Veit, B.. Forms and Integrations in Synthetic Differential Geometry, Aarhus preprint series 1979–80, no. 31.Google Scholar
[8] Lawvere, P. W.. Toward the description in a smooth topos of the dynamically possible motions and deformations of a continuous body. Cahiers Topologie Géom. Differentielle 21 (1980), 377–392.Google Scholar
[9] Menard, P.. El Ingenioso Hidalgo Don Quijote De La Mancha. Unfinished manuscript, partly edited by Borges, J. L..Google Scholar
[10] Moerdijk, I. and Reyes, G. E.. Smooth spaces versus continuous spaces in models for synthetic differential geometry. J. Pure Appl. Algebra (in the Press).Google Scholar
[11] Moerdijk, I. and Reyes, G. E.. Cohomology theories in synthetic differential geometry. In Proceedings of the Workshop on Category Theoretic Methods in Geometry, Aarhus 1983 (in the Press).Google Scholar
[12] Quê, N. van and Reyes, G. E.. Smooth functors and synthetic calculus. In The L. E. J. Brouwer Centenary Symposium, Studies in Logic vol. 110, ed. Troelstra, A. S. and van Dalen, D. (North-Holland, 1982), pp. 377–395.Google Scholar
[13] Reyes, G. E.. Théorie des modèles et faisceaux. Adv. Math. 30 (1978), 156–170.Google Scholar
[14] Weil, A.. Sur les théorèmes de De Rham. Comment. Math. Helv. 26 (1952), 119–145.Google Scholar