Floer homology

In mathematics, Floer homology refers to a family of homology theories which share similar characteristics and are believed by experts to be closely related. Some of these theories are due directly to Andreas Floer, while others are derived or inspired by his work. They are all modelled upon Morse homology on finite dimensional manifolds, extending it to the case where the relevant Morse function has finite relative indices. The differentials all count some sort of pseudoholomorphic curves.

Symplectic Field Theory

This is an invariant of contact manifolds and symplectic cobordisms between them, originally due to Yasha Eliashberg, Alexander Givental and Helmut Hofer. It includes a homology theory whose chains are generated by Reeb orbits and whose differentials count punctured holomorphic curves in the symplectization of a contact manifold.

Related Topics:
Contact manifold - Symplectic cobordism - Yasha Eliashberg - Alexander Givental - Helmut Hofer - Reeb orbit

~ ~ ~ ~ ~ ~ ~ ~ ~ ~