Inventiones mathematicae

, Volume 173, Issue 1, pp 209–223

Exotic smooth structures on small 4-manifolds


  • Anar Akhmedov
    • School of MathematicsGeorgia Institute of Technology
    • Department of Pure MathematicsUniversity of Waterloo

DOI: 10.1007/s00222-008-0118-x

Cite this article as:
Akhmedov, A. & Park, B. Invent. math. (2008) 173: 209. doi:10.1007/s00222-008-0118-x


Let M be either \(\mathbb{CP}^{2}\#3\overline{\mathbb{CP}}^{2}\) or \(3\mathbb{CP}^{2}\#5\overline{\mathbb{CP}}^{2}\). We construct the first example of a simply-connected irreducible symplectic 4-manifold that is homeomorphic but not diffeomorphic to M.

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© Springer-Verlag 2008