Floer homology of Hamiltonians supported on subsets
Floer homology is a fundamental construction relating dynamical properties of Hamiltonian flows on symplectic manifolds to the topology of the manifold. Although this construction is global in nature, when the Hamiltonian flow is supported on a subset one would like to "localize" this construction, or at least some of its consequences. I'll discuss several results in this direction. All symplectic preliminaries will be explained.