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

Karakurt, Çağri; Starkston, Laura

doi:10.2140/agt.2016.16.1585

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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

DOI: 10.2140/agt.2016.16.1585

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

Mathematical Subject Classification 2010

Primary: 53Dxx

Secondary: 57R57

References

Publication

Received: 8 October 2014

Revised: 15 September 2015

Accepted: 16 September 2015

Published: 1 July 2016

Authors

Çağri Karakurt
Department of Mathematics Bogazici University 34342 Istanbul Turkey

Laura Starkston
Mathematics Department Stanford University 450 Serra Mall, Building 380 Stanford, CA 78712-1202 United States

Volume 16, issue 3 (2016)