Hamiltonian pseudo-representations (Q1026413)

The reviewed article deals with the behaviour of the Poisson bracket under \(C^0\)-perturbations. The main result is that for any finite dimensional Lie algebra, the limit of a converging pseudo-representation is a representation. The consequence of this result is that for many non-closed syplectic manifolds the group of Hamiltonian diffeomorphisms has no \(C^{-1}\) bi-invariant metric. The new proof of the Gromov-Eliashberg theorem is given.