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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
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