Leaf-wise intersections and Rabinowitz Floer homology

TL;DR

This paper explores how Rabinowitz Floer homology can be used to prove the existence and multiplicity of leaf-wise intersection points in certain hypersurfaces within exact symplectic manifolds, advancing symplectic topology.

Contribution

It introduces a novel approach linking critical points of a perturbed Rabinowitz action functional to leaf-wise intersections, providing new existence and multiplicity results.

Findings

Existence of leaf-wise intersection points in hypersurfaces of restricted contact type.

Multiplicity results for leaf-wise intersections in exact symplectic manifolds.

Connection between Rabinowitz Floer homology and leaf-wise intersection theory.

Abstract

In this article we explain how critical points of a particular perturbation of the Rabinowitz action functional give rise to leaf-wise intersection points in hypersurfaces of restricted contact type. This is used to derive existence and multiplicity results for leaf-wise intersection points in hypersurfaces of restricted contact type in general exact symplectic manifolds. The notion of leaf-wise intersection points was introduced by Moser.