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 smooth embedding of connected sums of lens spaces in ${\mathbb{C}}^2$ can be upgraded to a Stein embedding, and determined that this never happens.

arXiv comment14 pages. V2: minor referee's corrections, suggestions and bibliographic updates. This version to appear in Michigan Mathematical Journal