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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The geography of irreducible 4-manifolds


Author: Jongil Park
Journal: Proc. Amer. Math. Soc. 126 (1998), 2493-2503
MSC (1991): Primary 57N13, 57R55
MathSciNet review: 1487335
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04762-5
PII: S 0002-9939(98)04762-5
Keywords: Fiber sum, irreducible manifold, rational blow-down
Received by editor(s): January 23, 1997
Communicated by: Leslie Saper
Article copyright: © Copyright 1998 American Mathematical Society