Inventiones mathematicae

, Volume 173, Issue 1, pp 209-223

First online:

Exotic smooth structures on small 4-manifolds

  • Anar AkhmedovAffiliated withSchool of Mathematics, Georgia Institute of Technology
  • , B. Doug ParkAffiliated withDepartment of Pure Mathematics, University of Waterloo  Email author 

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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.