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


Indecomposability of certain Lefschetz fibrations

Author: András I. Stipsicz
Journal: Proc. Amer. Math. Soc. 129 (2001), 1499-1502
MSC (2000): Primary 53C27
Published electronically: October 25, 2000
MathSciNet review: 1712877
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Abstract | References | Similar Articles | Additional Information


We prove that Lefschetz fibrations admitting a section of square $-1$ cannot be decomposed as fiber sums. In particular, Lefschetz fibrations on symplectic 4-manifolds found by Donaldson are indecomposable. This observation also shows that symplectic Lefschetz fibrations are not necessarily fiber sums of holomorphic ones.

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Additional Information

András I. Stipsicz
Affiliation: Department of Analysis, ELTE TTK, 1088. Múzeum krt. 6-8., Budapest, Hungary and Department of Mathematics, University of California, Irvine, California 92697

PII: S 0002-9939(00)05681-1
Keywords: 4-manifolds, Lefschetz fibrations, vanishing cycles
Received by editor(s): June 19, 1999
Received by editor(s) in revised form: August 16, 1999
Published electronically: October 25, 2000
Additional Notes: This research was supported by OTKA and Széchenyi Professzori Ösztöndíj.
Communicated by: Ronald Fintushel
Article copyright: © Copyright 2000 American Mathematical Society