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Article

Keywords:
general connection; tangent valued form; functorial prolongation; Weil functor
Summary:
We consider the problem of prolongating general connections on arbitrary fibered manifolds with respect to a product preserving bundle functor. Our main tools are the theory of Weil algebras and the Frölicher-Nijenhuis bracket.
References:
[1] Cabras, A., Kolář, I.: Prolongation of tangent valued forms to Weil bundles. Arch. Math. (Brno) 31 (1995), 139–145. MR 1357981
[2] Ehresmann, C.: Oeuvres complètes et commentés. Cahiers Topol. Géom. Diff. XXIV (Suppl. 1 et 2) (1983).
[3] Kolář, I.: Handbook of Global Analysis. ch. Weil Bundles as Generalized Jet Spaces, pp. 625–665, Elsevier, Amsterdam, 2008. MR 2389643
[4] Kolář, I.: On the functorial prolongations of fiber bundles. Miskolc Math. Notes 14 (2013), 423–431. DOI 10.18514/MMN.2013.903 | MR 3144079
[5] Kolář, I.: Covariant Approach to Weil Bundles. Folia, Masaryk University, Brno (2016).
[6] Kolář, I., Michor, P.W., Slovák, J.: Natural Operations in Differential Geometry. Springer Verlag, 1993.
[7] Mangiarotti, L., Modugno, M.: Graded Lie algebras and connections on a fibered space. J. Math. Pures Appl. (9) 63 (1984), 111–120.
[8] Weil, A.: Théorie des points proches sur les variétes différentielles. Colloque de topol. et géom. diff., Strasbourg (1953), 111–117.
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