The geography of irreducible 4-manifolds

Author:
Jongil Park

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

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we investigate the existence and the uniqueness problems for simply connected irreducible -manifolds. By taking fiber sums along an embedded surface of square and by a rational blow-down procedure, we construct many new irreducible -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 are covered by these irreducible -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:
https://doi.org/10.1090/S0002-9939-98-04762-5

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