Abstract
If ( X , ω ) is a closed symplectic manifold, and Σ is a smooth symplectic submanifold Poincaré dual to a positive multiple of ω, then X ∖ Σ can be completed to a Liouville manifold ( W , d λ ) . Under monotonicity assumptions on X and on Σ, we construct a chain complex whose homology computes the symplectic homology of W. We show that the differential is given in terms of Morse contributions, Gromov–Witten invariants of X relative to Σ and Gromov–Witten invariants of Σ. We use a Morse–Bott model for symplectic homology. Our proof involves comparing Floer cylinders with punctures to pseudoholomorphic curves in the symplectization of the unit normal bundle to Σ.
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