Volume 8, issue 3 (2008)

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Small exotic 4–manifolds

Anar Akhmedov

Algebraic & Geometric Topology 8 (2008) 1781–1794
Abstract

In this article, we construct the first example of a simply-connected minimal symplectic 4–manifold that is homeomorphic but not diffeomorphic to $3{ℂℙ}^{2}\phantom{\rule{0.3em}{0ex}}#7{\overline{ℂℙ}}^{2}$. We also construct the first exotic minimal symplectic ${ℂℙ}^{2}#5\phantom{\rule{0.3em}{0ex}}{\overline{ℂℙ}}^{2}$.

Keywords
4–manifolds, exotic smooth structures, symplectic 4–manifolds, fiber sum, Seiberg–Witten invariants
Mathematical Subject Classification 2000
Primary: 57N65, 57N13
Secondary: 57M50