In this paper we construct several irreducible 4-manifolds, both small and arbitrarily large, wit... more In this paper we construct several irreducible 4-manifolds, both small and arbitrarily large, with abelian non-cyclic fundamental group. The manufacturing procedure allows us to fill in numerous points in the geography plane of symplectic manifolds with π 1 = Z ⊕ Z, Z ⊕ Z p and Z q ⊕ Z p (gcd(p, q) = 1). We then study the botany of these points for π 1 = Z p ⊕ Z p .
Journal of the Australian Mathematical Society, 2011
In this paper we study the geography and botany of symplectic spin 4-manifolds with abelian funda... more In this paper we study the geography and botany of symplectic spin 4-manifolds with abelian fundamental group. Building on the constructions in [19] and [21], the techniques employed allow us to give alternative proofs and extend their results to the nonsimply connected realm.
In this note, four-manifold theory is employed to study the existence of (twisted) generalized co... more In this note, four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have more than one type change loci. In an example-driven fashion, (twisted) generalized complex structures are constructed on a myriad of four-manifolds, both simply and non-simply connected, which are neither complex nor symplectic.
In this paper we construct several irreducible 4-manifolds, both small and arbitrarily large, wit... more In this paper we construct several irreducible 4-manifolds, both small and arbitrarily large, with abelian non-cyclic fundamental group. The manufacturing procedure allows us to fill in numerous points in the geography plane of symplectic manifolds with π 1 = Z ⊕ Z, Z ⊕ Z p and Z q ⊕ Z p (gcd(p, q) = 1). We then study the botany of these points for π 1 = Z p ⊕ Z p .
Journal of the Australian Mathematical Society, 2011
In this paper we study the geography and botany of symplectic spin 4-manifolds with abelian funda... more In this paper we study the geography and botany of symplectic spin 4-manifolds with abelian fundamental group. Building on the constructions in [19] and [21], the techniques employed allow us to give alternative proofs and extend their results to the nonsimply connected realm.
In this note, four-manifold theory is employed to study the existence of (twisted) generalized co... more In this note, four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have more than one type change loci. In an example-driven fashion, (twisted) generalized complex structures are constructed on a myriad of four-manifolds, both simply and non-simply connected, which are neither complex nor symplectic.
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Papers by Rafael Torres