We construct a family version of symplectic Floer cohomology for magnetic cotangent bundles, without any restrictions on the magnetic form, using the dissipative method for compactness introduced by Groman (2023). As an application, we deduce that if N is a closed orientable manifold and σ is a magnetic form that is not weakly exact, then the π1-sensitive Hofer-Zehnder capacity of any compact set in the magnetic cotangent bundle determined by σ is finite.
Bibliographical notePublisher Copyright:
© 2023 Swiss Mathematical Society.
- family Floer theory
- Hofer-Zehnder capacity
- Twisted symplectic cohomology