Does anyone know if it is at all possible to relate a Lie dragged vector field (on a manifold) to the set of path homotopies on the underlying topological space of that manifold? They sure look alike to me, but I can find no reference either way.

I haven't posted any definitions, or the reasons for my question, assuming that anyone who can give an answer won't need them. But I am happy to do so, on request.

Not that that anyone is interested, but I'm now sure the answer is no, and that, in fact, the question was meaningless. Duh