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Soldered double linear morphisms. (English) Zbl 0763.53032

If \(T\) is the tangent functor, one defines the (second order lifting) functors \(TT^*\), \(T^*T\), \(T^*T^*\). The main result of this paper is concerned with a complete description of all the natural transformations of \(TT^*\) into itself. The method applied here is based on the concept of soldered double space fibrations and their morphisms. The paper contains also an extensive preliminary study of the previous fibrations on the local, say, level.

MSC:

53C05 Connections (general theory)
55R05 Fiber spaces in algebraic topology
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