Joint with John Etnyre, Hyunki Min, Lisa Piccirillo
Abstract: We present a handlebody construction of small symplectic caps, and hence of small closed symplectic 4-manifolds. We use this to construct handlebody descriptions of symplectic embeddings of rational homology balls in ℂP2, and thereby provide the first examples of (infinitely many) symplectic handlebody decompositions of a closed symplectic 4-manifold. Our constructions provide a new topological interpretation of almost toric fibrations of ℂP2 in terms of symplectic handlebody decompositions.
Link to arxiv.