Floer homology and stable Morse homology in symplectic geometry.

摘要

First part of this thesis develops Morse theory for generating functions of Lagrangian submanifolds in a cotangent bundle of a compact smooth manifold. The second part establishes the equality between the symplectic invariants constructed through Morse homology of generating functions and the ones defined through Floer homology. As a by-product, it is proved that there exists a level preserving isomorphism between the Morse homology of generating functions and the Floer homology for any closed submanifold of the base.