The geography of spin symplectic 4-manifolds (Q697336)

The author constructs simply connected spin symplectic (non-complex) 4-manifolds that realize all but finitely many lattice points \((\chi, {\mathbf c})\) lying in the region \(0\leq {\mathbf c}\leq 8.76\chi\), where \({\mathbf c}=c^2_1(X), \chi=\frac{1}{2}(1+b^{+}_2(X))\). These manifolds are obtained as fiber sums of the elliptic surface \(E(n)\), the Horikawa surface \(H(8k-1)\), the Brieskorn manifolds, and a complex surface of Persson-Peters-Xiao that has positive signature and contains a holomorphic curve of intersection \(0\). The manifolds are all homeomorphic to \((2m+1)S^2\times S^2\), but not diffeomorphic, for \(m\) large, as shown by using the Seiberg-Witten invariant surgery formula of \textit{R. Fintushel} and \textit{R. J. Stern} [Invent. Math. 134, 363-400 (1998; Zbl 0914.57015)].