Disjoinable Lagrangian spheres and dilations

Abstract

We consider open symplectic manifolds which admit dilations (in the sense previously introduced by Solomon and the author). We obtain restrictions on collections of Lagrangian submanifolds which are pairwise disjoint (or pairwise disjoinable by Hamiltonian isotopies) inside such manifolds. This includes the Milnor fibres of isolated hypersurface singularities which have been stabilized (by adding quadratic terms) sufficiently often.

v2: includes minor changes (mostly typos and grammar) as in the published version

References in corpus (2)

• Exact Lagrangian submanifolds in simply-connected cotangent bundles
• The Kunneth formula in Floer homology for manifolds with restricted contact type boundary

Cited by in corpus (11)

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• From symplectic cohomology to Lagrangian enumerative geometry
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• Picard-Lefschetz theory and dilating C^*-actions
• A Log PSS morphism with applications to Lagrangian embeddings
• Symplectic fillings of asymptotically dynamically convex manifolds I
• Floer cohomology of $\mathfrak{g}$-equivariant Lagrangian branes
• Koszul duality via suspending Lefschetz fibrations
• Disjoinable Lagrangian tori and semisimple symplectic cohomology
• On holographic duals of certain isolated weighted Gorenstein cDV singularities
• Persistence of unknottedness of clean Lagrangian intersections