New Exotic four-manifolds with $\mathbb{Z}/2\mathbb{Z}$ fundamental group

Abstract

We extend a construction of Stipsicz-Szabó of infinitely many irreducible exotic smooth structures of some closed four-manifolds with even $b_2^{+}$ and fundamental group $\mathbb{Z}/2\mathbb{Z}$. We use the double node surgery and rational blow down constructions of Fintushel-Stern on some elliptic fibrations equipped with a free involution. The construction is done in an equivariant manner and the factor manifolds are distinguished by the Seiberg-Witten invariants of their universal covers.

arXiv comment14 pages, 7 figures, to appear in Michigan Journal of Mathematics