The Geography of Spin Symplectic 4-Manifolds

Abstract

In this paper we construct a family of simply connected, spin, non-complex, symplectic 4-manifolds which cover all but finitely many allowed lattice points $(\chi ,c)$ lying in $0\le c\le 8.76\chi$. Furthermore, as a corollary, we prove that there exist infinitely many exotic smooth structures on $(2n+1)(S^2\times S^2)$ for all n large enough.

This is a revised version. AMS-LaTeX file, 13 pages with 2 eps-figures. Minor errors and grammatical problems are corrected. To appear in Mathematische Zeitschrift