Mathematical Research Letters

Volume 17 (2010)

Number 3

Geography of simply connected spin symplectic 4-manifolds

Pages: 483 – 492



Anar Akhmedov (University of Minnesota)

B. Doug Park (University of Waterloo)


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 $S^2\times S^2$.

Full Text (PDF format)