## Algebraic & Geometric Topology

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

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 16, Number 3 (2016), 1585-1635.

Dates
Revised: 15 September 2015
Accepted: 16 September 2015
First available in Project Euclid: 28 November 2017

https://projecteuclid.org/euclid.agt/1511895857

Digital Object Identifier
doi:10.2140/agt.2016.16.1585

Mathematical Reviews number (MathSciNet)
MR3523050

Zentralblatt MATH identifier
1350.57033

#### Citation

Karakurt, Çağri; Starkston, Laura. Surgery along star-shaped plumbings and exotic smooth structures on $4$–manifolds. Algebr. Geom. Topol. 16 (2016), no. 3, 1585--1635. doi:10.2140/agt.2016.16.1585. https://projecteuclid.org/euclid.agt/1511895857

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