, Volume 159, Issue 3, pp 657-667

Simply connected symplectic 4-manifolds with b 2 +=1 and c 1 2=2

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In this article we construct a new simply connected symplectic 4-manifold with b 2 +=1 and c 1 2=2 which is homeomorphic, but not diffeomorphic, to a rational surface by using rational blow-down technique. As a corollary, we conclude that a rational surface $\mathbf{C}P^{2}{\sharp} 7 \overline{\mathbf{C}P}^{2}$ admits an exotic smooth structure.

Mathematics Subject Classification (2000)

53D05, 14J26, 57R55, 57R57