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Exotic smooth structures on $3\mathbf{CP}^2 \char93 n\overline{\mathbf{CP}}^2$


Author: B. Doug Park
Journal: Proc. Amer. Math. Soc. 128 (2000), 3057-3065
MSC (2000): Primary 57R55; Secondary 57R57, 53D05.
DOI: https://doi.org/10.1090/S0002-9939-00-05357-0
Published electronically: March 2, 2000
Erratum: Proc. Amer. Math. Soc. 136 (2008), 1503-1503.
MathSciNet review: 1664426
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Abstract: We construct exotic $3\mathbf{CP}^2 \char93 10 \overline{\mathbf{CP}}^2$and $3\mathbf{CP}^2 \char93 12{\overline{\mathbf{CP}}}^2$ as a corollary of recent results of I. Dolgachev and C. Werner concerning a numerical Godeaux surface. We also construct another exotic $3\mathbf{CP}^2 \char93 12 {\overline{\mathbf{CP}}}^2$using the surgery techniques of R. Fintushel and R. J. Stern. We show that these 4-manifolds are irreducible by computing their Seiberg-Witten invariants.


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Additional Information

B. Doug Park
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: bahnpark@math.princeton.edu

DOI: https://doi.org/10.1090/S0002-9939-00-05357-0
Received by editor(s): August 4, 1998
Received by editor(s) in revised form: November 2, 1998
Published electronically: March 2, 2000
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society

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