Immersed Lagrangian Floer Theory

Understand

Let (M,w) be a compact symplectic manifold, and L a compact, embedded Lagrangian submanifold in M.

• Fukaya, Oh, Ohta and Ono construct Lagrangian Floer cohomology for such M,L, yielding groups HF^*(L,b;\Lambda) for one Lagrangian or HF^*((L,b),(L',b');\Lambda) for two, where b,b' are choices of bounding cochains, and exist if and only if L,L' have unobstructed Floer cohomology.
• These are independent of choices up to canonical isomorphism, and have important invariance properties under Hamiltonian equivalence.
• Floer cohomology groups are the morphism groups in the derived Fukaya category of (M,w), and so are an essential part of the Homological Mirror Symmetry Conjecture of Kontsevich.