Homology Spheres Bounding Acyclic Smooth Manifolds and Symplectic Fillings

Abstract

In this paper, we collect various structural results to determine when an integral homology 3-sphere bounds an acyclic smooth 4-manifold, and when this can be upgraded to a Stein manifold. In a different direction, we study whether a smooth embedding of connected sums of lens spaces in ${\mathbb{C}}^2$ can be upgraded to a Stein embedding, and we have determined that this never happens.