2018/04/30 by Luís Diogo, Samuel T. Lisi · 22 citations
Mathematics · #Bundle #Floer homology #Geometric and Algebraic Topology #Geometry and complex manifolds #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Normal bundle #Submanifold #Symplectic geometry #Symplectic manifold #Symplectomorphism #math.SG #msc:53D40 #msc:53D42 #msc:53D45
paper · pdf · doi:10.1112/topo.12105
published in Journal of Topology 12(3), 967-1030 (Wiley) · revisions thanks to feedback from referee, accepted in Journal of Topology
openalex created_date 2018/05/07 · arxiv created 2019/03/23 · openalex publication_date 2019/04/23 · arxiv updated 2019/09/25 · openalex updated_date 2026/08/05
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.