研究期間：10108~10207;In this research project, we focus on monotone Lagrangian tori of general dimensions, and study them from the perspective of surgery. In the first year we will develop surgical constructions of twist tori in R2n. For the second year we will explore new Hamiltonian isotopy invariants associated to the surgery. We will also examine the relation between the surgery and other invariants of Lagrangian submanifolds. Starting from the third year we will extend our study to the global case and exploring the interplay between the topology of symplectic manifolds and that of their monotone Lagrangian submanifolds. In the third year we will consider Stein manifolds and their monotone Lagrangian submanifolds. In the fourth year we will extend our investigation to the compact Kahler case. We will focus on some model examples including the projective spaces and product manifolds of spheres.
