A compact symplectic four-manifold admits only finitely many inequivalent toric actions
A compact symplectic four-manifold admits only finitely many inequivalent toric actions
Let ($M$, \omega) be a four-dimensional compact connected symplectic manifold. We prove that ($M$, \omega) admits only finitely many inequivalent Hamiltonian effective 2-torus actions. Consequently, if $M$ is simply connected, the number of conjugacy classes of 2-tori in the symplectomorphism group Sympl($M$, \omega) is finite. Our proof is “soft”. The …