Coisotropic submanifolds, leaf-wise fixed points, and presymplectic embeddings

Abstract

Let $(M,\omega)$ be a geometrically bounded symplectic manifold, $N\subseteq M$ be a closed, regular coisotropic submanifold, and $\phi:M\to M$ be a Hamiltonian diffeomorphism. The main result of this article is that the number of leafwise fixed points of $\phi$ is bounded below by the sum of the Betti numbers of $N$, provided that the Hofer distance between $\phi$ and the identity is small enough and the pair $(N,\phi)$ is non-degenerate. As an application, I prove a presymplectic non-embedding result. A version of the Arnold-Givental conjecture for coisotropic submanifolds is also discussed.