Geography of simply connected spin symplectic 4-manifolds, II

Simply Connected Symplectic 4-manifolds with B

In this article we construct a new family of simply connected symplectic 4-manifolds with b+2 = 1 and c 2 1 = 2 which are not diffeomorphic to rational surfaces by using rational blow-down technique. As a corollary, we conclude that a rational surface CP ♯7CP 2 admits an exotic smooth structure.

The Geography of Spin Symplectic 4-manifolds

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 (χ, c) lying in the region 0 ≤ c ≤ 8.76χ. Furthermore, as a corollary, we prove that there exist infinitely many exotic smooth structures on (2n+ 1)(S × S) for all n large enough.

Geography of Simply Connected Nonspin Symplectic 4-manifolds with Positive Signature

Simply Connected Symplectic Calabi-yau 6-manifolds

In this article, we construct simply connected symplectic Calabi-Yau 6-manifold by applying Gompf’s symplectic fiber sum operation along T. Using our method, we also construct symplectic nonKähler Calabi-Yau 6-manifolds with fundamental group Z. We also produce the first examples of simply connected symplectic Calabi-Yau and non-Calabi-Yau 6-manifolds via coisotropic Luttinger surgery on non si...

On Simply-connected 4-manifolds

This paper concerns (but does not succeed in performing) the diffeomorphism classification of closed, oriented, differential, simply-connected 4-manifolds. It arises out of the observation (due to Pontrjagin and Milnor [2]) that if two such manifolds Mx and M2 have isomorphic quadratic forms of intersection numbers on #2(Jft-), then there is a map / : M1-^-Mi which is a homotopy equivalence and...