arXiv subjects
Publications and source records attributed to Andrea Parma.
We use elementary arguments to prove that none of the Stein rational homology 4-balls shown by the authors and Brendan Owens to embed smoothly but not symplectically in the complex projective plane admit such almost complex embeddings. In particular, we are able to show that those rational balls admit no symplectic embeddings in the complex projective plane without appealing to the work of Evans-Smith.
We complete the classification of the smooth, closed, oriented 4-manifolds having Euler characteristic less than four and a horizontal handlebody decomposition of genus one. We use the classification result to find a large family of rational homology ball smoothings of cyclic quotient singularities which can be smoothly embedded into the complex projective plane. Our family contains all such rational balls previously known to embed into $\mathbb{CP}^2$ and infinitely many more. We also show that a rational ball of our family admits an almost-complex embedding in $\mathbb{CP}^2$ if and only if it admits a symplectic embedding.
We show that every smooth, closed, orientable 4-manifold X admits a special kind of handlebody decomposition that we call horizontal. We classify the closed 4-manifolds with the simplest horizontal decompositions and we describe all such decompositions of CP^2, showing that they give rise to infinitely many of the known embeddings of rational homology balls in the complex projective plane.
We extend recent work of Brendan Owens by constructing a doubly infinite family of Stein rational homology balls which can be smoothly but not symplectically embedded in CP^2.