Symplectic embeddings of 4-manifolds via Lefschetz fibrations

Abstract

In this article we study proper symplectic and iso-symplectic embeddings of 4–manifolds in 6–manifolds. We show that a closed orientable smooth 4–manifold admitting a Lefschetz fibration over CP 1 admits a symplectic embedding in the symplectic manifold (CP 1 × CP 1 × CP , ωpr), where ωpr is the product symplectic form on CP 1 ×CP 1 ×CP . We also show that there exists a sub-critical Weinstein 6–manifold in which all finite type Weinstein 4–manifolds admit iso-symplectic embeddings.