#### Volume 16, issue 3 (2016)

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Surgery along star-shaped plumbings and exotic smooth structures on $4$–manifolds

### Çağri Karakurt and Laura Starkston

Algebraic & Geometric Topology 16 (2016) 1585–1635
##### Abstract

We define a new $4$–dimensional symplectic cut and paste operation which is analogous to Fintushel and Stern’s rational blow-down. We use this operation to produce multiple constructions of symplectic smoothly exotic complex projective spaces blown up eight, seven, and six times. We also show how this operation can be used in conjunction with knot surgery to construct an infinite family of minimal exotic smooth structures on the complex projective space blown-up seven times.

##### Keywords
symplectic, exotic, rational blow-down, Seiberg–Witten
Primary: 53Dxx
Secondary: 57R57