Lagrangian submanifolds and Lefschetz pencils SG/0407126 16
نویسنده
چکیده
Given a Lagrangian submanifold in a symplectic manifold and a Morse function on the submanifold, we show that there is an isotopic Morse function and a symplectic Lefschetz pencil on the manifold extending the Morse function to the whole manifold. From this construction we define a sequence of symplectic invariants classifying the isotopy classes of Lagrangian spheres in a symplectic 4-manifold.
منابع مشابه
Lefschetz pencils and the canonical class for symplectic 4-manifolds
We present a new proof of a result due to Taubes: if (X,ω) is a closed symplectic four-manifold with b+(X) > 1 + b1(X) and λ[ω] ∈ H (X;Q) for some λ ∈ R, then the Poincaré dual of KX may be represented by an embedded symplectic submanifold. The result builds on the existence of Lefschetz pencils on symplectic four-manifolds. We approach the topological problem of constructing submanifolds with ...
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