Smooth embeddings of rational homology balls

The rational homology balls BnBn appeared in Fintushel and Sternʼs rational blow-down construction [3] and were subsequently used in [10] and [4] to construct exotic smooth manifolds with small Euler numbers. We show that a large class of smooth 4-manifolds have all the BnBns for odd n⩾3n⩾3 embedded in them. In particular, we give explicit examples, using Kirby calculus, of several families of smooth embeddings of the rational homology balls BnBn.