Journal of Symplectic Geometry

Volume 3 (2005)

Number 2

Lagrangian submanifolds and Lefschetz pencils

Pages: 171 – 219

DOI: http://dx.doi.org/10.4310/JSG.2005.v3.n2.a2

Authors

Vicente Muñoz

Francisco Presas

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.

Full Text (PDF format)