Geography and Botany of Irreducible Nonspin Symplectic 4-manifolds with Abelian Fundamental Group

On the Geography and Botany of Irreducible 4-manifolds with Abelian Fundamental Group

The geography and botany of smooth/symplectic 4-manifolds with cyclic fundamental group are addressed. For all the possible lattice points which correspond to non-spin manifolds of negative signature and a given homeomorphism type, an irreducible symplectic manifold and an infinite family of pairwise non-diffeomorphic non-symplectic irreducible manifolds are manufactured. In the same fashion, a...

Small Irreducible Symplectic 4-manifolds with Abelian Non-cyclic Fundamental Group

there exists a symplectic irreducible 4-manifold X with π1(X) = G and (c 2 1(X), χh(X)) = (c, χ). The characteristic numbers are given in terms of χh = 1/4(e+σ) and c 2 1 = 2e+3σ, where e is the Euler characteristic of the manifold X and σ its signature. To describe conditions under which smooth 4-manifolds are unique has been a theme in 4-manifold theory for quite some time. Besides its role i...

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

4-Manifolds with a Symplectic Bias

2 Symplectic 4-Manifolds 11 2.1 kähler structures & co. . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 geography and botany . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 pseudoholomorphic curves . . . . . . . . . . . . . . . . . . . . . 19 2.5 lefschetz pencils . . . . . . . . . . . . . . . . . . . . . . . ...

New symplectic 4-manifolds with nonnegative signature

We construct new families of symplectic 4-manifolds with nonnegative signature that are interesting with respect to the geography problem. In particular, we construct an irreducible symplectic 4-manifold that is homeomorphic to mCP#mCP for each odd integer m satisfying m ≥ 49.