Remarks on symplectic circle actions, torsion and loops

Abstract

We study loops of symplectic diffeomorphisms of closed symplectic manifolds. Our main result, which is valid for a large class of symplectic manifolds, shows that the flux of a symplectic loop vanishes whenever its orbits are contractible. As a consequence, we obtain a new vanishing result for the flux group and new instances where the presence of a fixed point of a symplectic circle action is a sufficient condition for it to be Hamiltonian. We also obtain applications to symplectic torsion, more precisely, non-trivial elements of ${\mathrm{Symp}}_0(M,\omega )$ that have finite order.

16 pages

References in corpus (3)

• Free circle actions with contractible orbits on symplectic manifolds
• Rectangular diagrams of surfaces: the basic moves
• Non-Hamiltonian actions with fewer isolated fixed points