Revista de la
Unión Matemática Argentina
The natural operators lifting $q$-forms to $p$-forms on Weil bundles
Włodzimierz M. Mikulski

Volume 69, no. 1 (2026), pp. 161–178    

Published online (final version): December 26, 2025

https://doi.org/10.33044/revuma.4796

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Abstract

Let $q,p,k, m$ be positive integers with $m\geq k+p +1$, and let $A$ be a Weil algebra with $k$ generators. The (not necessarily regular) natural operators lifting $q$-forms on an $m$-dimensional manifold $M$ to $p$-forms on the Weil bundle $T^AM$ are completely described by means of the so-called excellent maps. As a consequence, we show that any natural operator lifting $q$-forms on an $m$-dimensional manifold $M$ to $p$-forms on $T^AM$ is regular, i.e., it sends smoothly parametrized families into smoothly parametrized families. We apply our general results to the case where $T^A$ is the $r$th- order tangent bundle $T^rM=J^r_0(\mathbf{R},M)$ (in particular, the tangent bundle).

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