Journal of Symplectic Geometry

Volume 3 (2005)

Number 2

Lagrangian submanifolds and Lefschetz pencils

Pages: 171 – 219



Vicente Muñoz

Francisco Presas


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.

Published 1 January 2005