Note on coisotropic Floer homology and leafwise fixed points · arXivDesk
1707.04478Jul 14, 201711 pages. I have split this article off from "Leafwise fixed points for $C^0$-small Hamiltonian flows" arXiv:1408.4578 . version 2: I included a definition of Floer homology for an adiscal or monotone regular coisotropic submanifold
Note on coisotropic Floer homology and leafwise fixed points
For an adiscal or monotone regular coisotropic submanifold N of a symplectic manifold I define its Floer homology to be the Floer homology of a certain Lagrangian embedding of N. Given a Hamiltonian isotopy φ=(φt) and a suitable almost complex structure, the corresponding Floer chain complex is generated by the (N,φ)
Nearby in the stack
-contractible leafwise fixed points. I also outline the construction of a local Floer homology for an arbitrary closed coisotropic submanifold. Results by Floer and Albers about Lagrangian Floer homology imply lower bounds on the number of leafwise fixed points. This reproduces earlier results of mine. The first construction also gives rise to a Floer homology for a Boothby-Wang fibration, by applying it to the circle bundle inside the associated complex line bundle. This can be used to show that translated points exist.