More Brieskorn spheres bounding rational balls
Oguz Savk

TL;DR
This paper introduces new families of Brieskorn spheres that non-trivially bound rational homology balls, expanding the known examples and providing simpler proofs of classical results in the field.
Contribution
It presents novel infinite families of Brieskorn spheres bounding rational homology balls and simplifies existing proofs of classical results.
Findings
New families: xt(2,4n+3,12n+7) and xt(3,3n+2,12n+7) for even n
Revisits and simplifies classical results on Brieskorn spheres bounding integral homology balls
Extends the understanding of which Brieskorn spheres bound rational homology balls
Abstract
We call an integral homology sphere bounds a rational homology ball if it is obstructed from bounding an integral homology ball. After Fintushel and Stern's well-known example , Akbulut and Larson recently provided the first infinite families of Brieskorn spheres non-trivially bounding rational homology balls: and for odd~. Using their technique, we present new such families: and for even . 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.
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