Narrow Results

A central problem in low-dimensional topology asks which homology three-spheres bound contractible four-manifolds or homology four-balls. In this paper, we address this question for plumbed three-manifolds and we present two new infinite families. We consider most of the classical examples from around the 1980s by reproving that they all bound Mazur manifolds. We also show that several well-known families bound possibly different types of four-manifolds, called Poénaru homology four-balls. To unify classical and new results in a fairly simple way, we modify Mazur’s argument and work with Poénaru manifolds.