On the underlying lower order bundle functors

Miroslav Doupovec

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 4, page 901-916
  • ISSN: 0011-4642

Abstract

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For every bundle functor we introduce the concept of subordinated functor. Then we describe subordinated functors for fiber product preserving functors defined on the category of fibered manifolds with m -dimensional bases and fibered manifold morphisms with local diffeomorphisms as base maps. In this case we also introduce the concept of the underlying functor. We show that there is an affine structure on fiber product preserving functors.

How to cite

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Doupovec, Miroslav. "On the underlying lower order bundle functors." Czechoslovak Mathematical Journal 55.4 (2005): 901-916. <http://eudml.org/doc/30997>.

@article{Doupovec2005,
abstract = {For every bundle functor we introduce the concept of subordinated functor. Then we describe subordinated functors for fiber product preserving functors defined on the category of fibered manifolds with $m$-dimensional bases and fibered manifold morphisms with local diffeomorphisms as base maps. In this case we also introduce the concept of the underlying functor. We show that there is an affine structure on fiber product preserving functors.},
author = {Doupovec, Miroslav},
journal = {Czechoslovak Mathematical Journal},
keywords = {bundle functor; Weil bundle; natural transformation; bundle functor; Weil bundle; natural transformation},
language = {eng},
number = {4},
pages = {901-916},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the underlying lower order bundle functors},
url = {http://eudml.org/doc/30997},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Doupovec, Miroslav
TI - On the underlying lower order bundle functors
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 4
SP - 901
EP - 916
AB - For every bundle functor we introduce the concept of subordinated functor. Then we describe subordinated functors for fiber product preserving functors defined on the category of fibered manifolds with $m$-dimensional bases and fibered manifold morphisms with local diffeomorphisms as base maps. In this case we also introduce the concept of the underlying functor. We show that there is an affine structure on fiber product preserving functors.
LA - eng
KW - bundle functor; Weil bundle; natural transformation; bundle functor; Weil bundle; natural transformation
UR - http://eudml.org/doc/30997
ER -

References

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  1. 10.1007/s006050170010, Monatsh. Math. 134 (2001), 39–50. (2001) MR1872045DOI10.1007/s006050170010
  2. 10.1017/S0027763000007339, Nagoya Math.  J. 158 (2000), 99–106. (2000) MR1766571DOI10.1017/S0027763000007339
  3. A general point of view to nonholonomic jet bundles, Cahiers Topo. Geom. Diff. Categoriques XLIV (2003), 149–160. (2003) MR1985835
  4. Natural Operations in Differential Geometry, Springer-Verlag, 1993. (1993) MR1202431
  5. 10.1016/S0926-2245(99)00022-4, Diff. Geom. Appl. 11 (1999), 105–115. (1999) MR1712139DOI10.1016/S0926-2245(99)00022-4
  6. On the simplicial structure of some Weil bundles, Rend. Circ. Mat. Palermo, Serie  II, Suppl. 63 (2000), 131–140. (2000) MR1758088
  7. The Method of Iterated Tangents with Applications in Local Riemannian Geometry, Pitman Press, , 1982. (1982) Zbl0478.58002MR0693620

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