Non-displaceable contact embeddings and infinitely many leaf-wise intersections

TL;DR

This paper constructs a broad class of contact manifolds with properties ensuring non-displaceability and infinitely many leaf-wise intersections, revealing deep symplectic topology phenomena.

Contribution

It introduces a method using Lefschetz fibrations to produce contact manifolds with non-displaceability and infinite leaf-wise intersections, expanding understanding of symplectic topology.

Findings

Any bounding contact embedding is non-displaceable.

Such manifolds have infinitely many leaf-wise intersection points.

Stein fillings have infinite dimensional symplectic homology.

Abstract

We construct using Lefschetz fibrations a large family of contact manifolds with the following properties: Any bounding contact embedding into an exact symplectic manifold satisfying a mild topological assumption is non-displaceable and generically has infinitely many leaf-wise intersection points. Moreover, any Stein filling has infinite dimensional symplectic homology.