An example of symplectic 4-manifolds with positive signature

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

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...

Symplectic 4-manifolds with Arbitrary Fundamental Group near the Bogomolov-miyaoka-yau Line Scott Baldridge and Paul Kirk

In this paper we construct a family of symplectic 4–manifolds with positive signature for any given fundamental group G that approaches the BMY line. The family is used to show that one cannot hope to do better than than the BMY inequality in finding a lower bound for the function f = χ+ bσ on the class of all minimal symplectic 4-manifolds with a given fundamental group.

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.

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).