# EXOTIC SMOOTH STRUCTURE ON ℂℙ2#13ℂℙ2

• Cho, Yong-Seung (Department of Mathematics Ehwa Women's University) ;
• Hong, Yoon-Hi (National Institute for Mathematical Sciences)
• Published : 2006.07.01
• 118 11

#### Abstract

In this paper, we construct a new exotic smooth 4-manifold X which is homeomorphic, but not diffeomorphic, to ${\mathbb{C}}\mathbb{P}^2{\sharp}13\overline{\mathbb{C}\mathbb{P}}^2$. Moreover the manifold X has vanishing Seiberg-Witten invariants for all $Spin^c$-structures of X and has no symplectic structure.

#### Keywords

Seiberg-Witten invariant;symplectic 4-manifold;antisymplectic involution;double branched cover

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