Small exotic rational surfaces without 1- and 3-handles. (English) Zbl 1210.57030
Theorem: For \(7\leq n \leq 9\), there exists a smooth 4-manifold that is homeomorphic but not diffeomorphic to \(\mathbb CP^2\#n \overline{\mathbb CP^2}\) and has neither 1- nor 3-handles in a handle decomposition. Furthermore, there exists a smooth 4-manifold that is homeomorphic but not diffeomorphic to \(\mathbb CP^2\#6\overline{\mathbb CP^2}\) and has no 1-handles in a handle decomposition.
The method of the construction uses rational blowdowns (Fintushel-Stern). Also, the author proposes a strategy of applications of rational blowdowns for construction of exotic \(\mathbb CP^2\#n\overline{\mathbb CP^2}\), \(n\leq 9\).
The method of the construction uses rational blowdowns (Fintushel-Stern). Also, the author proposes a strategy of applications of rational blowdowns for construction of exotic \(\mathbb CP^2\#n\overline{\mathbb CP^2}\), \(n\leq 9\).
Reviewer: Yuli Rudyak (Gainesville)
MSC:
| 57R55 | Differentiable structures in differential topology |
| 57R65 | Surgery and handlebodies |
| 57N13 | Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010) |
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