Fiber product preserving bundle functors on all morphisms of fibered manifolds

Ivan Kolář; Włodzimierz M. Mikulski

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 3, page 285-293
  • ISSN: 0044-8753

Abstract

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We describe the fiber product preserving bundle functors on the category of all morphisms of fibered manifolds in terms of infinite sequences of Weil algebras and actions of the skeleton of the category of r -jets by algebra homomorphisms. We deduce an explicit formula for the iteration of two such functors. We characterize the functors with values in vector bundles.

How to cite

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Kolář, Ivan, and Mikulski, Włodzimierz M.. "Fiber product preserving bundle functors on all morphisms of fibered manifolds." Archivum Mathematicum 042.3 (2006): 285-293. <http://eudml.org/doc/249781>.

@article{Kolář2006,
abstract = {We describe the fiber product preserving bundle functors on the category of all morphisms of fibered manifolds in terms of infinite sequences of Weil algebras and actions of the skeleton of the category of $r$-jets by algebra homomorphisms. We deduce an explicit formula for the iteration of two such functors. We characterize the functors with values in vector bundles.},
author = {Kolář, Ivan, Mikulski, Włodzimierz M.},
journal = {Archivum Mathematicum},
keywords = {fiber product preserving bundle functor; Weil algebra; $r$-jet; Weil algebra; -jet},
language = {eng},
number = {3},
pages = {285-293},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Fiber product preserving bundle functors on all morphisms of fibered manifolds},
url = {http://eudml.org/doc/249781},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Kolář, Ivan
AU - Mikulski, Włodzimierz M.
TI - Fiber product preserving bundle functors on all morphisms of fibered manifolds
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 3
SP - 285
EP - 293
AB - We describe the fiber product preserving bundle functors on the category of all morphisms of fibered manifolds in terms of infinite sequences of Weil algebras and actions of the skeleton of the category of $r$-jets by algebra homomorphisms. We deduce an explicit formula for the iteration of two such functors. We characterize the functors with values in vector bundles.
LA - eng
KW - fiber product preserving bundle functor; Weil algebra; $r$-jet; Weil algebra; -jet
UR - http://eudml.org/doc/249781
ER -

References

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  1. Cabras A., Kolář I., Flow prolongation of some tangent valued forms, to appear in Acta Mathematica Sinica. MR2411105
  2. Doupovec M., Kolář I., Iteration of fiber product preserving bundle functors, Monatsh. Math. 134 (2001), 39–50. Zbl0999.58001MR1872045
  3. Kolář I., Functorial prolongations of Lie algebroids, Proceedings Conf. Prague 2004, Charles University, Prague, 2005, 301–309. MR2268942
  4. Kolář I., Functorial prolongations of Lie groupoids, to appear in Banach Center Publications. Zbl1115.58003MR2342859
  5. Kolář I., Cabras A., On the functorial prolongations of principal bundles, to appear in CMUC. Zbl1150.58002MR2337425
  6. Kolář I., Michor P. W., Slovák J., Natural Operations in Differential Geometry, Springer-Verlag, 1993. (1993) MR1202431
  7. Kolář I., Mikulski W. M., On the fiber product preserving bundle functors, Differential Geometry and Its Applications 11 (1999), 105–115. (1999) Zbl0935.58001MR1712139
  8. Mikulski W. M., There exists a prolongation functor of infinite order, Časopis pěst. mat. 114 (1989), 57–59. (1989) Zbl0672.58002MR0990118
  9. Mikulski W. M., Natural transformations of Weil functors into bundle functors, Rend. Circ. Mat. Palermo (2), Suppl. 22 (1989), 177–191. (1989) MR1061799
  10. Weil A., Théorie des points proches sur les variétes différentielles, Colloque de topol. et géom. diff., Strasbourg (1953), 111–117. (1953) MR0061455

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