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Indecomposability of certain Lefschetz fibrations
Author(s):
András
I.
Stipsicz
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1499-1502.
MSC (2000):
Primary 53C27
Posted:
October 25, 2000
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Abstract:
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.
References:
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- [D]
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- R. Fintushel and R. Stern, Constructions of smooth 4-manifolds, Proc. Internat. Cong. Math. (Berlin, 1998), Vol II, Doc. Math. Extra Volume ICMII (1998), 443-452. MR 99g:57033
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- R. Gompf and A. Stipsicz, 4-Manifolds and Kirby calculus, AMS Grad. Studies in Math. vol. 20 (1999).
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- R. Gompf, A new construction of symplectic manifolds, Ann. of Math. 142 (1995), 527-595. MR 96j:57025
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- B. Ozbagci and A. Stipsicz, Noncomplex smooth 4-manifolds with genus-2 Lefschetz fibrations, Proc. Amer. Math. Soc., to appear. CMP 99:07
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- D. Salamon, Spin geometry and Seiberg-Witten invariants, book in preparation.
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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:
10.1090/S0002-9939-00-05681-1
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
Posted:
October 25, 2000
Additional Notes:
This research was supported by OTKA and Széchenyi Professzori Ösztönd{í}j.
Communicated by:
Ronald Fintushel
Copyright of article:
Copyright
2000,
American Mathematical Society
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