The York map is a canonical transformation (Q1074147)

A fundamental object of study in the Einstein theory of gravity is the York map, which in the vacuum case is a map from the freely chosen conformal data (i.e. pairs (3-metric, transverse traceless, conjugate momentum)) to the space of constraint satisfying physical data (analogously for the vacuum case). Introduced in a Hamiltonian context, the question of whether the York map is a symplectic one or not naturally arises. This work demonstrates that the York map is a degenerate symplectic map, the domain and range of which are presymplectic varieties. Passing to suitable quotients, a nondegenerate York map between symplectic varieties is obtained.