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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2006; 43(4): 691-701

Printed July 1, 2006

Copyright © The Korean Mathematical Society.

Exotic smooth structure on $\Bbb {CP}^2\sharp 13 \overline {\Bbb {CP}}^2$

Yong Seung Cho and Yoon Hi Hong

Ehwa Women's University, National Institute for Mathematical Sciences

Abstract

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In this paper, we construct a new exotic smooth 4-manifold $X$ which is homeomorphic, but not diffeomorphic, to $\Bbb {CP}^2 \sharp 13\overline {\Bbb {CP}}^2.$ 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, anti-symplectic involution, double branched cover

MSC numbers: 14J27, 14J28, 53D05, 57M12, 57M60, 57R20, 57R57

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