Symplectic embeddings of 4-manifolds via Lefschetz fibrations

Dishant M. Pancholi; Francisco Presas

Symplectic embeddings of 4-manifolds via Lefschetz fibrations

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arxiv 2110.12950 v1 pith:QFPGSOTZ submitted 2021-10-25 math.GT math.SG

Dishant M. Pancholi , Francisco Presas This is my paper · ORCID

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keywords symplecticmanifoldstimesembeddingsmanifoldiso-symplecticlefschetzomega

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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 $\C P^1$ admits a symplectic embedding in the symplectic manifold $(\C P^1 \times \C P^1 \times \C P^1, \omega_{pr}),$ where $\omega_{pr}$ is the product symplectic form on $\C P^1 \times \C P^1 \times \C P^1.$ We also show that there exists a sub-critical Weinstein $6$--manifold in which all finite type Weinstein $4$--manifolds admit iso-symplectic embeddings.

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