Smooth embeddings of rational homology balls

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