Lagrangian bubmanifolds of products of spheres

Abstract

This work investigates certain Lagrangian submanifolds of products of spheres. In particular, we will study several constructions of "exotic" Lagrangian tori in S^2 x S^2, and we will prove that they are all Hamiltonian isotopic. In the space (S^2)^3, we will investigate a Lagrangian submanifold that is diffeomorphic to RP^3, and we will prove that it is nondisplaceable under Hamiltonian diffeomorphisms by showing that the homology of a certain chain complex (called the pearl complex) is non-trivial.