On the action spectrum for closed symplectically aspherical manifolds 论文

摘要

Symplectic homology is studied on closed symplectic manifolds where the class of the symplectic form and the first Chern class vanish on the second homotopy group. Critical values of the action functional are associated to cohomology classes of the manifold. Those lead to continuous sections in the action spectrum bundle. The action of the cohomology ring via the cap-action and the pants-product on the set of critical values is studied and a bi-invariant metric on the group of Hamiltonian symplectomorphisms is defined and analyzed. Finally, a relative symplectic capacity is defined which is bounded below by the π1-sensitive Hofer-Zehnder capacity. As an application it is proven that a Hamiltonian automorphism whose support has finite such capacity has infinitely many nontrivial geometrically distinct periodic points. 1. Overview of the Results.