Synthetic differential geometry of higher-order total differentials

Hirokazu Nishimura

Cahiers de Topologie et Géométrie Différentielle Catégoriques (2006)

  • Volume: 47, Issue: 3, page 207-232
  • ISSN: 1245-530X

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Nishimura, Hirokazu. "Synthetic differential geometry of higher-order total differentials." Cahiers de Topologie et Géométrie Différentielle Catégoriques 47.3 (2006): 207-232. <http://eudml.org/doc/91707>.

@article{Nishimura2006,
author = {Nishimura, Hirokazu},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {synthetic differential geometry; total differentials; tangentials; microcubes},
language = {eng},
number = {3},
pages = {207-232},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Synthetic differential geometry of higher-order total differentials},
url = {http://eudml.org/doc/91707},
volume = {47},
year = {2006},
}

TY - JOUR
AU - Nishimura, Hirokazu
TI - Synthetic differential geometry of higher-order total differentials
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 2006
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 47
IS - 3
SP - 207
EP - 232
LA - eng
KW - synthetic differential geometry; total differentials; tangentials; microcubes
UR - http://eudml.org/doc/91707
ER -

References

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  2. [2] Kock, A.: A simple axiomatics for differentiation, Math. Scand., 40 (1977), 183-193. Zbl0375.12029MR453845
  3. [3] Kock, A.: Taylor series calculus for ring objects of line type, Journal of Pure and Applied Algebra, 12 (1978), 271-293. Zbl0394.14003MR501073
  4. [4] Kock, A.: Synthetic Differential Geometry, London Mathematical Society Lecture Note Series, 51, Cambridge University Press, Cambridge, 1981. Zbl0466.51008MR649622
  5. [5] Lavendhomme, R.: Basic Concepts of Synthetic Differential Geometry, Kluwer, Dordrecht, 1996. Zbl0866.58001MR1385464
  6. [6] Libermann, P.: Sur les prolongements de fibrés principaux et des groupoïdes différentiables banachiques, Analyse Globale, 7-108, PressesUniv. Montréal, Montréal, Quebec, 1971. Zbl0248.53031MR356117
  7. [7] Moerdijk, I. and Reyes, G.E.: Models for Smooth Infinitesimal Analysis, Springer-Verlag, New York, 1991. Zbl0715.18001MR1083355
  8. [8] Navarro, J.A. and Sancho de Salas, J.B.: C∞-Differentiable Spaces, Lecture Notes in Mathematics, 1824, Springer-Verlag, Berlin and Heidelberg, 2003. Zbl1039.58001
  9. [9] Nishimura, H.: Theory of microcubes, International Journal of TheoreticalPhysics, 36 (1997), 1099-1131. Zbl0884.18014MR1452238
  10. [10] Nishimura, H.: Synthetic differential geometry of jet bundles, Bull. Belg. Math. Soc. Simon Stevin, 8 (2001), 639-650. Zbl1030.58001MR1875384
  11. [11] Nishimura, H.: Corrigenda to "Synthetic differential geometry of jet bundles", Bull. Belg. Math. Soc. Simon Stevin, 9 (2002), 473. Zbl1030.58001MR2016586
  12. [12] Nishimura, H.: Holonomicity in sythetic differential geometry of jet bundles, Beiträge zur Algebra und Geometrie, 44 (2003), 471-481. Zbl1044.58006MR2017047
  13. [13] Nishimura, H.: Higher-order preconnections in synthetic differential geometry of jet bundles, Beiträge zur Algebra und Geometrie, 45 (2004), 677-696. Zbl1071.58004MR2093035
  14. [14] Saunders, D.J.: The Geometry of Jet Bundles, London Mathematical Society Lecture Note Series, 142, Cambridge University Press, Cambridge, 1989. Zbl0665.58002MR989588

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