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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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