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 Exotic smooth structures on $(2n+2l-1)\mathbb{CP}^2 \sharp (2n+4l-1)\overline{\mathbb{CP}}^2$ Bull. Korean Math. Soc. 2010 Vol. 47, No. 5, 961-971 https://doi.org/10.4134/BKMS.2010.47.5.961Published online September 1, 2010 Jongil Park and Ki-Heon Yun Seoul National University, Sungshin Women's University Abstract : As an application of `reverse engineering' technique introduced by R. Fintushel, D. Park and R. Stern [9], we present a simple way to construct an infinite family of exotic $(2n+2l-1)\mathbb{CP}^2 \sharp (2n+4l-1) \overline{\mathbb{CP}}^2$'s for all $n \ge 0,\, l \ge 1$. Keywords : exotic smooth structure, Luttinger surgery, symplectic fiber sum MSC numbers : 57R17, 57R57, 57N13 Full-Text :