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Constructing jet bundles from a cocycle of smooth transition functions
concepts of jet prolongations of principal bundles, so to a principal bundle $P$ you can associate a $k$-th jet prolongation $P^{(k)}$, which has a larger structure group (basically the group of $k$-jets … The corresponding transition functions basically can be viewed as the $k$-jets of the initial transition functions, and this construction is compatible (more or less by construction) with equivalence of …