More Brieskorn spheres bounding rational balls

Abstract

We call an integral homology sphere $\text{non-trivially}$ bounds a rational homology ball if it is obstructed from bounding an integral homology ball. After Fintushel and Stern's well-known example $\Sigma (2,3,7)$, Akbulut and Larson recently provided the first infinite families of Brieskorn spheres non-trivially bounding rational homology balls: $\Sigma (2,4n+1,12n+5)$ and $\Sigma (3,3n+1,12n+5)$ for odd~$n$. Using their technique, we present new such families: $\Sigma (2,4n+3,12n+7)$ and $\Sigma (3,3n+2,12n+7)$ for even $n$. Also manipulating their main argument, we simply recover some classical results of Akbulut and Kirby, Fickle, Casson and Harer, and Stern about Brieskorn spheres bounding integral homology balls.

11 pages, 10 figures; minor corrections and clarifications