Preprint 45/1997

A capacity for closed symplectically aspherical manifolds

Matthias Schwarz

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Submission date: 18. Dec. 1997
Pages: 34

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 X1-sensitive Hofer-Zehnder capacity.

24.11.2021, 02:10