The symplectic cohomology of magnetic cotangent bundles

Abstract

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  is a magnetic form that is not weakly exact, then the ${\pi }_1$ 1-sensitive Hofer–Zehnder capacity of any compact set in the magnetic cotangent bundle determined by $\sigma$ is finite.