Symplectic diffeomorphisms and the flux homomorphism (Q793351)

Let \((X,\omega)\) be a symplectic manifold. We study a certain countable subgroup \(\Gamma_{\omega}\) of \(H^ 1_ c(X;{\mathbb{R}})\) which measures the indeterminacy of the flux homomorphism. As an application, we show that the inclusion of the group of all compactly supported symplectic diffeomorphisms of X into the group of all compactly supported diffeomorphisms is not always a homotopy equivalence.