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Natural transformations of Weil functors into bundle functors. (English) Zbl 0715.57013
Geometry and physics, Proc. 9th Winter Sch., Srní/Czech. 1989, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 22, 177-191 (1990).
[For the entire collection see Zbl 0699.00032.]
Natural transformations of the Weil functor \(T^ A\) of A-velocities [I. Kolař, Commentat. Math. Univ. Carol. 27, 723-729 (1986; Zbl 0603.58001)] into an arbitrary bundle functor F are characterized. In the case where F is a linear bundle functor, the author deduces that the dimension of the vector space of all natural transformations of \(T^ A\) into F is finite and is less than or equal to \(\dim (F_ 0{\mathbb{R}}^ k)\). The spaces of all natural transformations of Weil functors into linear functors of higher order tangent bundles are determined.
Reviewer: J.Kubarski

MSC:
57R22 Topology of vector bundles and fiber bundles
55R10 Fiber bundles in algebraic topology
58A20 Jets in global analysis