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 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

Email:
stipsicz@cs.elte.hu, astipsic@math.uci.edu

DOI:
https://doi.org/10.1090/S0002-9939-00-05681-1

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