Symplectic rigidity and weak commutativity (Q362544)

A celebrated theorem of Gromov and Eliashberg states that if a uniform limit of symplectic diffeomorphisms is a diffeomorphism, then it is symplectic. The authors give a short proof of this theorem based on the \(C^0\)-rigidity of the Poisson bracket, discovered by \textit{F. Cardin} and \textit{C. Viterbo} [Duke Math. J. 144, No. 2, 235--284 (2008; Zbl 1153.37029)].