Exotic smooth structures on $3\mathbf {CP}^2 \# n\overline {\mathbf {CP}}^2$
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- by B. Doug Park
- Proc. Amer. Math. Soc. 128 (2000), 3057-3065
- DOI: https://doi.org/10.1090/S0002-9939-00-05357-0
- Published electronically: March 2, 2000
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Erratum: Proc. Amer. Math. Soc. 136 (2008), 1503-1503.
Abstract:
We construct exotic $3\mathbf {CP}^2 \# 10 \overline {\mathbf {CP}}^2$ and $3\mathbf {CP}^2 \# 12{\overline {\mathbf {CP}}}^2$ as a corollary of recent results of I. Dolgachev and C. Werner concerning a numerical Godeaux surface. We also construct another exotic $3\mathbf {CP}^2 \# 12 {\overline {\mathbf {CP}}}^2$ 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.References
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Bibliographic Information
- B. Doug Park
- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
- Email: bahnpark@math.princeton.edu
- 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
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1664426