Double node neighborhoods and families of simply connected 4-manifolds with b^+=1

Ronald Fintushel; Ronald J. Stern

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arXiv · math/0412126

Double node neighborhoods and families of simply connected 4-manifolds with b^+=1

Ronald Fintushel·Ronald J. Stern

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Abstract

We introduce a new technique that is used to show that the complex projective plane blown up at 6, 7, or 8 points has infinitely many distinct smooth structures. None of these smooth structures admit smoothly embedded spheres with self-intersection -1, i.e. they are minimal. In addition, none these smooth structures admit an underlying symplectic structure. Shortly after the appearance of a preliminary version of this article, Park, Stipsicz, and Szabo used the techniques described herein to show that the complex projective plane blown up at 5 points has infinitely many distinct smooth structures. In the final section of this paper we give a somewhat different construction of such a family of examples.

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BibTeX RIS

Ronald Fintushel, Ronald J. Stern. 2005-01-18. Double node neighborhoods and families of simply connected 4-manifolds with b^+=1. https://arxiv.org/abs/math/0412126

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