Four-manifolds up to connected sum with complex projective planes

Self-duality and Differentiable Structures on the Connected Sum of Complex Projective Planes

It is proved that if the twistor space of a self-dual four-manifold of positive scalar curvature contains a real effective divisor of degree two, then the four-manifold is difFeomorphic to the connected sum nCP2 of n complex projective planes for some n . It follows that if the four-manifold is known to be homeomorphic to 4CP2 , then it is also difFeomorphic to 4CP2 .

Area-minimizing Projective Planes in Three-manifolds

A diffeomorphism classification of manifolds which are like projective planes

We give a complete diffeomorphism classification of 1-connected closed manifolds M with integral homology H∗(M) ∼= Z ⊕ Z ⊕ Z, provided that dim(M) 6= 4. The integral homology of an oriented closed manifold1 M contains at least two copies of Z (in degree 0 resp. dimM). IfM is simply connected and its homology has minimal size (i.e., H∗(M) ∼= Z⊕Z), then M is a homotopy sphere (i.e., M is homotopy...

Decomposing Four-Manifolds up to Homotopy Type

Let M be a closed connected oriented topological 4-manifold with fundamental group π1. Let Λ be the integral group ring of π1. Suppose that f : M → P is a degree one map inducing an isomorphism on π1. We give a homological condition on the intersection forms λM and λ Λ M under which M is homotopy equivalent to a connected sum P#M ′ for some simply-connected closed (non-trivial) topological 4-ma...

Dynamics of Automorphisms on Projective Complex Manifolds

We show that the dynamics of automorphisms on all projective complex manifolds X (of dimension 3, or of any dimension but assuming the Good Minimal Model Program or Mori’s Program) are canonically built up from the dynamics on just three types of projective complex manifolds: complex tori, weak Calabi-Yau manifolds and rationally connected manifolds. As a by-product, we confirm the conjecture o...