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Noncomplex smooth 4-manifolds with genus-2 Lefschetz fibrations

Author(s): Burak Ozbagci; András I. Stipsicz
Journal: Proc. Amer. Math. Soc. 128 (2000), 3125-3128.
MSC (2000): Primary 57R55; Secondary 57R65, 57M50
Posted: April 28, 2000
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Abstract:

We construct noncomplex smooth 4-manifolds which admit genus-2 Lefschetz fibrations over $S^2$. The fibrations are necessarily hyperelliptic, and the resulting 4-manifolds are not even homotopy equivalent to complex surfaces. Furthermore, these examples show that fiber sums of holomorphic Lefschetz fibrations do not necessarily admit complex structures.

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Additional Information:

Burak Ozbagci
Affiliation: Department of Mathematics, University of California Irvine, Irvine, California 92697
Address at time of publication: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: bozbagci@math.uci.edu, bozbagci@math.msu.edu

András I. Stipsicz
Affiliation: Department of Analysis, ELTE TTK, Múzeum krt. 6-8, Budapest, Hungary
Email: stipsicz@cs.elte.hu

DOI: 10.1090/S0002-9939-00-05390-9
PII: S 0002-9939(00)05390-9
Keywords: Lefschetz fibrations, 4-manifolds, complex structures
Received by editor(s): October 13, 1998
Received by editor(s) in revised form: November 24, 1998
Posted: April 28, 2000
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 2000, American Mathematical Society

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The following works have cited this article

Siebert, Bernd; Tian, Gang , On hyperelliptic $C\sp \infty$-Lefschetz fibrations of four-manifolds, Commun. Contemp. Math 1 (1999), 255--280.

Gompf, Robert E.; Stipsicz, András I., $4$-manifolds and Kirby calculus, American Mathematical Society, 1999.

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