Geodesic
Double node neighborhoods and families of simply connected 4-manifolds with 𝑏⁺=1
Fintushel, Ronald 1   ; Stern, Ronald 2
1 Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
2 Department of Mathematics, University of California, Irvine, California 92697
Journal of the American Mathematical Society, Tome 19 (2006) no. 1, pp. 171-180 Cet article a éte moissonné depuis la source American Mathematical Society

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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 admits smoothly embedded spheres with self-intersection $-1$, i.e., they are minimal. In addition, none of these smooth structures admits 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 construction of such a family of examples.
DOI : 10.1090/S0894-0347-05-00500-X

Fintushel, Ronald  1   ; Stern, Ronald  2

1 Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
2 Department of Mathematics, University of California, Irvine, California 92697 
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Fintushel, Ronald; Stern, Ronald. Double node neighborhoods and families of simply connected 4-manifolds with 𝑏⁺=1. Journal of the American Mathematical Society, Tome 19 (2006) no. 1, pp. 171-180. doi: 10.1090/S0894-0347-05-00500-X

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