Maybe this question is rather too general to mention, but I hope the community can help to make it more precise in case it's needed.
The question is: if there's any link between the local conformal transformations of the Euclidean plane and the (local) diffeomorphisms of locally Lorentzian 4-manifolds?
In the answer to this question: Difference Between Algebra of Infinitesimal Conformal Transformations & Conformal Algebra, Qmechanic has alleged that the local (anti-)holomorphic maps on a Riemann sphere form a groupoid, isomorphic to the locally defined orientation-preserving conformal transformations.
Does it help with breaking down the (local) diffeomorphism group of the Lorentzian 4-manifold in terms of the local conformal group of the Euclidean plane?
