Hamiltonian Floer cohomology was invented by A. Floer to prove the Arnold conjecture: a Hamiltonian diffemorphism of a closed symplectic manifold has at least as many periodic orbits as the sum of the Betti numbers. A variant called Symplectic cohomology was later defined for certain non compact manifolds, including the  cotangent bundle of an arbitrary closed smooth manifold. The latter is the setting for classical mechanics of constrained systems. A particularly beautiful result is the Viterbo isomorphism equating the Symplectic cohomology of the cotangent bundle with homology of its free loop space. After reviewing these, I will discuss a generalization of Viterbo's isomorphism to classical mechanics in the presence of magnetic forces. Joint with Will J. Merry.

https//arxiv.org/abs/1809.01085