Algebraic & Geometric Topology

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

Çağri Karakurt and Laura Starkston

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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

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

Received: 8 October 2014
Revised: 15 September 2015
Accepted: 16 September 2015
First available in Project Euclid: 28 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53Dxx: Symplectic geometry, contact geometry [See also 37Jxx, 70Gxx, 70Hxx]
Secondary: 57R57: Applications of global analysis to structures on manifolds, Donaldson and Seiberg-Witten invariants [See also 58-XX]

symplectic exotic rational blow-down Seiberg–Witten


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.

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