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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The geography of irreducible 4-manifolds
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by Jongil Park PDF
Proc. Amer. Math. Soc. 126 (1998), 2493-2503 Request permission

Abstract:

In this paper we investigate the existence and the uniqueness problems for simply connected irreducible $4$-manifolds. By taking fiber sums along an embedded surface of square $0$ and by a rational blow-down procedure, we construct many new irreducible $4$-manifolds which have infinitely many distinct smooth structures. Furthermore, we prove that all but at most finitely many lattice points lying in the non-positive signature region with $2e+3 sign \geq 0$ are covered by these irreducible $4$-manifolds.
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Additional Information
  • Jongil Park
  • Affiliation: Department of Mathematics, University of California Irvine, Irvine, California 92697-3875
  • Address at time of publication: Department of Mathematics, Kon-Kuk University, Kwangjin-gu Mojin-dong 93-1, Seoul 143-701, Korea
  • Email: jpark@math.uci.edu, jipark@kkucc.konkuk.ac.kr
  • Received by editor(s): January 23, 1997
  • Communicated by: Leslie Saper
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 2493-2503
  • MSC (1991): Primary 57N13, 57R55
  • DOI: https://doi.org/10.1090/S0002-9939-98-04762-5
  • MathSciNet review: 1487335