The natural transformations $T^* T^{(r)}\to T^* T^{(r)}$

Abstract

For natural numbers $r\geq 1$ and $n\geq 3$ a complete classification of natural transformations $A:T^*T^{(r)}\to T^*T^{(r)}$ over $n$-manifolds is given, where $T^{(r)}$ is the linear $r$-tangent bundle functor.