Exotic smooth structures on $(2n+2l-1)\mathbb{CP}^2 \sharp (2n+4l-1)\overline{\mathbb{CP}}^2$

Jongil Park; Ki-Heon Yun

doi:10.4134/BKMS.2010.47.5.961

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2010; 47(5): 961-971

Printed September 1, 2010

https://doi.org/10.4134/BKMS.2010.47.5.961

Exotic smooth structures on $(2n+2l-1)\mathbb{CP}^2 \sharp (2n+4l-1)\overline{\mathbb{CP}}^2$

Jongil Park and Ki-Heon Yun

Seoul National University, Sungshin Women's University

Abstract

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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