Note on coisotropic Floer homology and leafwise fixed points

Abstract

<p style='text-indent:20px;'>For an adiscal or monotone regular coisotropic submanifold <inline-formula><tex-math id="M1">$ N $</tex-math></inline-formula> of a symplectic manifold I define its Floer homology to be the Floer homology of a certain Lagrangian embedding of <inline-formula><tex-math id="M2">$ N $</tex-math></inline-formula>. Given a Hamiltonian isotopy <inline-formula><tex-math id="M3">$ \varphi = ( \varphi^t) $</tex-math></inline-formula> and a suitable almost complex structure, the corresponding Floer chain complex is generated by the <inline-formula><tex-math id="M4">$ (N, \varphi) $</tex-math></inline-formula>-contractible leafwise fixed points. I also outline the construction of a local Floer homology for an arbitrary closed coisotropic submanifold.</p><p style='text-indent:20px;'>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.</p><p style='text-indent:20px;'>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.</p>