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

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Abstract

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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Authors and Affiliations

  1. Department of Mathematical Sciences, Seoul National University, San 56-1, Shinlim-dong, Kwanak-gu, Seoul, 151-747, Korea

    Jongil Park

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  1. Jongil Park
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Correspondence to Jongil Park.

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Mathematics Subject Classification (2000)

53D05, 14J26, 57R55, 57R57

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Park, J. Simply connected symplectic 4-manifolds with b2+=1 and c12=2. Invent. math. 159, 657–667 (2005). https://doi.org/10.1007/s00222-004-0404-1

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  • DOI: https://doi.org/10.1007/s00222-004-0404-1

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