We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
45/1997
A capacity for closed symplectically aspherical manifolds
Matthias Schwarz
Abstract
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 capaction and the pants-product on the set of critical values is studied and a biinvariant metric on the group of Hamiltonian symplectomorphisms is defined and analyzed. Finally, a relative symplectic capacity is defined which can be estimated by the $\pi_1$-sensitive Hofer-Zehnder capacity.
