Small exotic 4-manifolds with \(b_2^+=3\). (English) Zbl 1094.57027
Summary: We construct an infinite family of simply connected, pairwise nondiffeomorphic 4-manifolds, all homeomorphic to \(3{\mathbb {CP}}^2 \# 9 {\overline {{\mathbb C}{\mathbb P}^2}}\). Similar ideas provide examples of 4-manifolds with \(b_2^+=3\), \(b_2^-=8\), vanishing first homology and nontrivial Seiberg-Witten invariants.
MSC:
| 57R55 | Differentiable structures in differential topology |
| 57R57 | Applications of global analysis to structures on manifolds |
| 57N13 | Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010) |
