Using rational homology circles to construct rational homology balls

Abstract

Motivated by Akbulut-Larson's construction of Brieskorn spheres bounding rational homology 4-balls, we explore plumbed 3-manifolds that bound rational homology circles and use them to construct infinite families of rational homology 3-spheres that bound rational homology 4-balls. In particular, we find infinite families of torus bundles over the circle that bound rational homology circles provide a simple method for constructing many more plumbed 3-manifolds that bound rational homology circles. Using these rational homology circles, we show that, for example, −1-surgery along any twisted positively-clasped Whitehead double of any knot bounds a rational homology 4-ball.