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 space blown-up eight times, seven times, 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.

35 pages, 20 figures; v2 has significantly more examples of small exotic symplectic 4-manifolds including exotic CP2 blown up 6 and 7 times and the structure of the paper is reorganized; v3 corrects minor errors and some inconsistencies in conventions

References in corpus (4)

• Exotic Smooth Structures on Small 4-Manifolds
• HF = ECH via open book decompositions: a summary
• A symplectic manifold homeomorphic but not diffeomorphic to CP^2 # 3(-CP^2)
• Comparing star surgery to rational blow-down

Cited by in corpus (4)

• Using rational homology circles to construct rational homology balls
• Comparing star surgery to rational blow-down
• Deformation of Singular Fibers of Genus $2$ Fibrations and Small Exotic Symplectic $4$-Manifolds
• Kodaira Dimension in Low Dimensional Topology