The symplectic cohomology of magnetic cotangent bundles

2018/09/04 by Yoel Groman, Groman, Yoel, Will J. Merry +1 · 1 citation
Mathematics · #37J45 #53D40 #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1809.01085

openalex publication_date 2018/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 in \citeGroman2015. As an application, we deduce that if N is a closed 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.

Cited by

• Symplectic cohomology with support and aspherical perturbations

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