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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 | References | Similar Articles | Additional Information


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?)

  • 1. W. Barth, C. Peters and A. Van de Ven, Compact complex surfaces, Springer-Verlag, 1984. MR 86c:32026
  • 2. R. Friedman and J. Morgan, Smooth four-manifolds and complex surfaces, Springer-Verlag, 1994. MR 95m:57046
  • 3. R. Fintushel and R. Stern, Private communication.
  • 4. R. Gompf, Nuclei of elliptic surfaces, Topology 30 (1991), pp. 479-511. MR 92f:57042
  • 5. R. Gompf and A. Stipsicz, An introduction to 4-manifolds and Kirby calculus, AMS Graduate Studies in Math., vol. 20, 1999.
  • 6. Y. Matsumoto, Lefschetz fibrations of genus two - a topological approach, Proceedings of the 37th Taniguchi Symposium on Topology and Teichmüller Spaces, ed. Sadayoshi Kojima et al., World Scientific (1996), pp. 123-148. CMP 99:06
  • 7. I. Smith, Symplectic geometry of Lefschetz fibrations, Dissertation, Oxford, 1998.

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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

András I. Stipsicz
Affiliation: Department of Analysis, ELTE TTK, Múzeum krt. 6-8, Budapest, Hungary

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

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