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Article

Mikulski, Włodzimierz M.
The natural transformations $TT^{(r)}\to TT^{(r)}$. (English). Archivum Mathematicum, vol. 36 (2000), issue 1, pp. 71-75
MSC: 53A55, 58A20, 58A32 | MR 1751615 | Zbl 1049.58009
Keywords:
bundle functors; natural transformations
Summary:
For natural numbers $r\ge 2$ and $n$ a complete classification of natural transformations $A:TT^{(r)}\rightarrow TT^{(r)}$ over $n$-manifolds is given, where $T^{(r)}$ is the linear $r$-tangent bundle functor.
References:
[1] Gancarzewicz, J., Kolář, I.: Natural affinors on the extended $r$-th order tangent bundles. Suppl. Rendiconti Circolo Mat. Palermo 30 (1993), 95–100. MR 1246623
[2] Kolář I., Michor P. W., Slovák J.: Natural operations in differential geometry. Springer-Verlag, Berlin 1993. MR 1202431
[3] Zajtz, A.: On the order of natural operators and liftings. Ann. Polon. Math. 49 (1988), 169–178. MR 0983220
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