Rabinowitz Floer homology and mirror symmetry

Abstract

We define a quantitative invariant of Liouville cobordisms with monotone filling through an action-completed symplectic cohomology theory. We illustrate the non-trivial nature of this invariant by computing it for annulus subbundles of the tautological bundle over $\mathbb{C}{P}^1$ and give further conjectural computations based on mirror symmetry. We prove a non-vanishing result in the presence of Lagrangian submanifolds with non-vanishing Floer homology.

37 pages, 10 figures

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Cited by in corpus (9)

• Floer theory and reduced cohomology on open manifolds
• Mayer-Vietoris property for relative symplectic cohomology
• Homological mirror symmetry without corrections
• Multiplicative structures on cones and duality
• Rabinowitz Floer homology of negative line bundles and Floer Gysin sequence
• Reduced symplectic homology and string topology
• Computing the Rabinowitz Floer homology of tentacular hyperboloids
• On the Filtered Symplectic Homology of Prequantization Bundles
• Periodic leaf-wise intersection points from Lagrangians