Small exotic 4–manifolds

Akhmedov, Anar

doi:10.2140/agt.2008.8.1781

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Small exotic 4–manifolds

Anar Akhmedov

Algebraic & Geometric Topology 8 (2008) 1781–1794

DOI: 10.2140/agt.2008.8.1781

Abstract

In this article, we construct the first example of a simply-connected minimal symplectic 4–manifold that is homeomorphic but not diffeomorphic to $3 {ℂ ℙ}^{2} # 7 {\bar{ℂ ℙ}}^{2}$ . We also construct the first exotic minimal symplectic ${ℂ ℙ}^{2} # 5 {\bar{ℂ ℙ}}^{2}$ .

Keywords

4–manifolds, exotic smooth structures, symplectic 4–manifolds, fiber sum, Seiberg–Witten invariants

Mathematical Subject Classification 2000

Primary: 57N65, 57N13

Secondary: 57M50

References

Publication

Received: 12 March 2007

Revised: 7 July 2008

Accepted: 5 September 2008

Published: 9 October 2008

Authors

Anar Akhmedov
Mathematics Department Columbia University New York NY 10027 USA

Volume 8, issue 3 (2008)