Classical and new plumbed homology spheres bounding contractible manifolds and homology balls

Abstract

A central problem in low-dimensional topology asks which homology $3$-spheres bound contractible $4$-manifolds or homology $4$-balls. In this paper, we address this question for plumbed $3$-manifolds and we present two new infinite families. We consider most of the classical examples from around the nineteen eighties by reproving that they all bound Mazur manifolds. We also show that several well-known families bound possibly different types of $4$-manifolds, called Po\'enaru homology $4$-balls. To unify classical and new results in a fairly simple way, we modify Mazur's argument and work with Po\'enaru manifolds.