Holomorphic spheres and four-dimensional symplectic pairs

TL;DR

This paper classifies four-dimensional manifolds with symplectic pairs that contain embedded symplectic spheres with non-negative self-intersection, extending McDuff's classification to this new setting.

Contribution

It introduces a classification of 4D symplectic manifolds with symplectic pairs and embedded spheres, providing a new perspective in symplectic topology.

Findings

Classification of manifolds with symplectic pairs and embedded spheres

Extension of McDuff's classification to symplectic pairs

Identification of conditions for non-negative self-intersection spheres

Abstract

We classify four-dimensional manifolds endowed with symplectic pairs admitting embedded symplectic spheres with non-negative self-intersection, following the strategy of McDuff's classification of rational and ruled symplectic four manifolds.