Inventiones mathematicae

, Volume 159, Issue 3, pp 657–667

Simply connected symplectic 4-manifolds with b2+=1 and c12=2


    • Department of Mathematical SciencesSeoul National University

DOI: 10.1007/s00222-004-0404-1

Cite this article as:
Park, J. Invent. math. (2005) 159: 657. doi:10.1007/s00222-004-0404-1


In this article we construct a new simply connected symplectic 4-manifold with b2+=1 and c12=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.

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© Springer-Verlag 2004