Families of monotone symplectic manifolds constructed via symplectic cut and their Lagrangian submanifolds

Abstract

We describe families of monotone symplectic manifolds constructed via the symplectic cutting procedure of Lerman [Math. Res. Lett. 2 (1995) 247–258] from the cotangent bundle of manifolds endowed with a free circle action. We also give obstructions to the monotone Lagrangian embedding of some compact manifolds in these symplectic manifolds.