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Noncomplex smooth 4-manifolds with genus-2 Lefschetz fibrations


Authors: Burak Ozbagci and András I. Stipsicz
Journal: Proc. Amer. Math. Soc. 128 (2000), 3125-3128
MSC (2000): Primary 57R55; Secondary 57R65, 57M50
Published electronically: April 28, 2000
MathSciNet review: 1670411
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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.


References [Enhancements On Off] (What's this?)

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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: https://doi.org/10.1090/S0002-9939-00-05390-9
Keywords: Lefschetz fibrations, 4-manifolds, complex structures
Received by editor(s): October 13, 1998
Received by editor(s) in revised form: November 24, 1998
Published electronically: April 28, 2000
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society