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We present a handlebody construction of small symplectic caps, and hence ofsmall closed symplectic 4-manifolds. We use this to construct handlebodydescriptions of symplectic embeddings of rational homology balls in$\mathbb{C}\mathrm{P}^2$, and thereby provide the first examples of (infinitelymany) symplectic handlebody decompositions of a closed symplectic 4-manifold.Our constructions provide a new topological interpretation of almost toricfibrations of $\mathbb{C}\mathrm{P}^2$ in terms of symplectic handlebodydecompositions.

Small symplectic caps and embeddings of homology balls in the complex projective plane