Simply Connected Symplectic 4-manifolds with B

6 M ay 2 00 7 SIMPLY CONNECTED MINIMAL SYMPLECTIC 4 - MANIFOLDS WITH SIGNATURE LESS THAN – 1

For each pair (e, σ) of integers satisfying 2e + 3σ ≥ 0, σ ≤ −2, and e + σ ≡ 0 (mod 4), with four exceptions, we construct a minimal, simply connected symplectic 4-manifold with Euler characteristic e and signature σ. We also produce simply connected, minimal symplectic 4-manifolds with signature zero (resp. signature −1) with Euler characteristic 4k (resp. 4k + 1) for all k ≥ 46 (resp. k ≥ 49).

On symplectic 4-manifolds and contact 5-manifolds

In this thesis we prove some results on symplectic structures on 4-dimensional manifolds and contact structures on 5-dimensional manifolds. We begin by discussing the relation between holomorphic and symplectic minimality for Kähler surfaces and the irreducibility of minimal simply-connected symplectic 4-manifolds under connected sum. We also prove a result on the conformal systoles of symplect...

Spin symplectic 4-manifolds near Bogomolov-Miyaoka-Yau line

We construct the first known family of simply connected spin symplectic 4-manifolds Mk satisfying c 2 1 (Mk)/χh(Mk) → 9 as k → ∞. Using Mk, we also construct many other new spin symplectic 4-manifolds with nonnegative signature.

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...