Smooth Embeddings of Rational Homology Balls

Tatyana Khodorovskiy

paper

Smooth Embeddings of Rational Homology Balls

arXiv:1212.4391

Abstract

The rational homology balls $B_{n}$ appeared in Fintushel and Stern's rational blow-down construction [FS] and were subsequently used (e.g. Fintushel-Stern[FS4], Park[Pa2]) to construct exotic smooth manifolds with small Euler numbers. We show that a large class of smooth 4-manifolds have all of the $B_{n}$ 's for odd $n \geq 3$ embedded in them. In particular, we give explicit examples, using Kirby calculus, of several families of smooth embeddings of the rational homology balls $B_{n}$ .

15 pages, 40 figures