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.
