Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-24T02:26:17.319Z Has data issue: false hasContentIssue false
  • English
  • Français

Lie group valued integration in well-adapted toposes

Published online by Cambridge University Press:  17 April 2009

Anders Kock
Anders Kock
Affiliation:
Matematisk Institut, Aarhus University, Ny Munkegade, 8000 Aarhus C. Danmark
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the context of synthetic differential geometry, we prove that group valued 1-forms on the unit interval are exact, provided the group in question is a Lie group. This exactness is the basic assumption in a previous paper by the author on differential forms with values in groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 3 , December 1986 , pp. 395 - 410
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Belair, Luc, Calcul infinitesimal en gometrie differentielle synthetique, (M.Sc. Thesis, Univ. de Montréal, 08. 1981).Google Scholar
[2]Bruno, Oscar P., “Vector fields on RR in well adapted models of synthetic differential geometry”, J. Pure Appl. Algebra 41 (1986).Google Scholar
[3]Bruno, Oscar P., “A property of ideals of differentiate functions”, Bull. Austral. Math. Soc. 33 (1986), 293–305.CrossRefGoogle Scholar
[4]Dubuc, E.J., “C∞ schemes”, Amer. J. Math. 103 (1981), 683–690.CrossRefGoogle Scholar
[5]Frölicher, A., “Applications lisses entre espaces et variétés de Frechet”, C. R. Acad. Sci. Paris Sér. I Math. 293 (1981), 125–127.Google Scholar
[6]Frölicher, A., Gisin, B. and Kriegl, A., “General differentiation theory” in Category Theoretic Methods in Geometry, (Aarhus, Various Publ. Series 35 1983).Google Scholar
[7]Kock, A., Synthetic Differential Geometry, (London Math. soc. Publ. Series 51 Cambridge Univ. Press 1981).Google Scholar
[8]Kock, A., “Differential forms with values in groups”, Bull. Austral. Math. Soc. 25 (1982), 357–386.CrossRefGoogle Scholar
[9]Kock, A., “A combinatorial theory of connections”, in Mathematical Applications of Category Theory, Gray, J. (Ed.) (Contemp. Math. Vol. 30 1984), 132–144.CrossRefGoogle Scholar
[10]Kock, A., “Combinatorial notations relating to principal fibre bundles”, J. Pure Appl. Algebra 39 (1986), 141–151.CrossRefGoogle Scholar
[11]Kock, A., “Convenient vector spaces embed into the Cahiers topos”, Cahiers Topologie Géom. Différentielle 27 (1986).Google Scholar
[12]Kock, A., “Calculus of smooth functions between convenient vector spaces”, Aarhus Preprint Series 18 (1984/1985).Google Scholar
[13]Kock, A. and Reyes, G.E., “Models for synthetic integration theory”. Math. Scand. 48 (1981), 145–152.CrossRefGoogle Scholar
[14]Kriegl, A., “Eine kartesisch abegeschlossene Kategorie glatter Abbildungen zwischen beliebigen lokalkonvexen Vektorräumen”, Monatsh. Math. 95 (1983), 287–309.CrossRefGoogle Scholar
[15]Moerdijk, I. and Reyes, G.E., C ∞-rings (to appear).Google Scholar
[16]Reyes, G.E. and Van Que, N., “Smooth functors and synthetic calculus”, (The L.E.J. Brouwer Centenary Symposium, Troelstra, A.A. and van Dalen, D. (Eds.) North Holland, 1982), 377–398.Google Scholar