Isomorphism between Morse and Lagrangian Floer cohomol- ogy rings

The support of top graded local cohomol- ogy modules

Morse-Conley-Floer Homology

For Morse-Smale pairs on a smooth, closed manifold the MorseSmale-Witten chain complex can be defined. The associated Morse homology is isomorphic to the singular homology of the manifold and yields the classical Morse relations for Morse functions. A similar approach can be used to define homological invariants for isolated invariant sets of flows on a smooth manifold, which gives an analogue ...

Floer homology and Novikov rings

We prove the Arnold conjecture for compact symplectic manifolds under the assumption that either the first Chern class of the tangent bundle vanishes over π2(M) or the minimal Chern number is at least half the dimension of the manifold. This includes the important class of CalabiYau manifolds. The key observation is that the Floer homology groups of the loop space form a module over Novikov’s r...

On the Floer homology of cotangent bundles

This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle T M of a compact orientable manifold M . The first result is a new L estimate for the solutions of the Floer equation, which allows to deal with a larger and more natural class of Hamiltonians. The second and main result is a new construction of the isomorphism between the Fl...

Morse theory and Floer homology Meknès , 2012 Mihai Damian

The two theories we will describe in these lectures have many things in common. They both associate algebraic invariants to some geometric objects. The meaning of ”invariant” is that the algebraic object which is the outcome of the theory only depends on the initial geometric data and not on the methods specific to the theory. In other words, the invariant measures some quantity related to the ...