Surgeries on torus knots, rational balls, and cabling

We classify which positive integral surgeries on positive torus knots bound rational homology balls. Additionally, for a given knot K we consider which cables K p , q admit integral surgeries that bound rational homology balls. For such cables, let 𝒮 ( K ) be the set of corresponding rational numbers q p . We show that 𝒮 ( K ) is bounded for each K . Moreover, if n -surgery on K bounds a rational homology ball then n is an accumulation point for 𝒮 ( K ) .