Characterization of some natural transformations between the bundle functors T^{A}\circ T^{\ast} and T^{\ast}\circ T^{A} on Mf

Abstract

In this paper, we characterize some natural transformations between the bundle functors T^{A}\circ T^{\ast} and T^{\ast}\circ T^{A} on Mf_{m}. In the particular case where A is the space of r-jets at 0 of smooth maps of R --> R, we determine all of these natural transformations. In application, lifts of 1-forms are studied wuth application to the theory of presymplectic structures.