  When the vacuum Einstein equations are cast in the form of hamiltonian
evolution equations, the initial data lie in the cotangent bundle of the
manifold M\Sigma\ of riemannian metrics on a Cauchy hypersurface \Sigma. As in
every lagrangian field theory with symmetries, the initial data must satisfy
constraints. But, unlike those of gauge theories, the constraints of general
relativity do not arise as momenta of any hamiltonian group action. In this
paper, we show that the bracket relations among the constraints of general
relativity are identical to the bracket relations in the Lie algebroid of a
groupoid consisting of diffeomorphisms between space-like hypersurfaces in
spacetimes. A direct connection is still missing between the constraints
themselves, whose definition is closely related to the Einstein equations, and
our groupoid, in which the Einstein equations play no role at all. We discuss
some of the difficulties involved in making such a connection.
