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Lagrangian submanifolds and Lefschetz pencils

Denis Auroux·Vicente Muñoz·Francisco Presas
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Abstract

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.

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Denis Auroux, Vicente Muñoz, Francisco Presas. 2004-07-08. Lagrangian submanifolds and Lefschetz pencils. https://arxiv.org/abs/math/0407126

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