Geography of simply connected spin symplectic 4-manifolds

We present an algorithm that produces new families of closed simply connected spin symplectic\/ $4$-manifolds with nonnegative signature that are interesting with respect to the symplectic geography problem. In particular, for each odd integer $q$\/ satisfying $q\geq 275$, we construct infinitely many pairwise nondiffeomorphic irreducible smooth structures on the topological\/ $4$-manifold $q(S^2\times S^2)$, the connected sum of $q$\/ copies of $S^2\times S^2$.

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Published 1 January 2010