Compactly supported Hamiltonian diffeomorphism group
= Compactly supported Hamiltonian diffeomorphism group
{title2=$\operatorname{Ham}_c(M,\omega)$}
This subgroup uses Hamiltonians whose support in $[0,1]\times M$ is compact. Their flows are the identity outside a fixed compact set. On closed manifolds this support condition imposes no extra restriction. On an open <symplectic manifold>, it excludes nontrivial whole-fiber <cotangent fiber translations>, even when their generating one-form is exact.