Irreducible 4-manifolds with abelian non-cyclic fundamental group of small rank. (English) Zbl 1187.57022
Summary: 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 \(\pi_1 = \mathbb Z \oplus \mathbb Z,\mathbb Z \oplus \mathbb Z_p \) and \(\mathbb Z_q \oplus \mathbb Z_q (\gcd(p,q)\neq 1)\). We then study the botany of these points for \(\pi_1 = \mathbb Z_p \oplus \mathbb Z_q\).
MSC:
| 57N13 | Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010) |
| 57M05 | Fundamental group, presentations, free differential calculus |
| 57R55 | Differentiable structures in differential topology |
| 57R17 | Symplectic and contact topology in high or arbitrary dimension |
| 57M50 | General geometric structures on low-dimensional manifolds |
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