Indecomposability of certain Lefschetz fibrations
HTML articles powered by AMS MathViewer
- by András I. Stipsicz PDF
- Proc. Amer. Math. Soc. 129 (2001), 1499-1502 Request permission
Abstract:
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.References
- S. K. Donaldson, Lefschetz fibrations in symplectic geometry, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), 1998, pp. 309–314. MR 1648081
- Ronald Fintushel and Ronald J. Stern, Constructions of smooth $4$-manifolds, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), 1998, pp. 443–452. MR 1648094
- R. Gompf and A. Stipsicz, 4-Manifolds and Kirby calculus, AMS Grad. Studies in Math. vol. 20 (1999).
- Robert E. Gompf, A new construction of symplectic manifolds, Ann. of Math. (2) 142 (1995), no. 3, 527–595. MR 1356781, DOI 10.2307/2118554
- B. Ozbagci and A. Stipsicz, Noncomplex smooth 4-manifolds with genus-2 Lefschetz fibrations, Proc. Amer. Math. Soc., to appear.
- D. Salamon, Spin geometry and Seiberg-Witten invariants, book in preparation.
- I. Smith, Symplectic geometry of Lefschetz fibrations, Dissertation, Oxford 1998.
- I. Smith, in preparation.
- András Stipsicz, A note on the geography of symplectic manifolds, Turkish J. Math. 20 (1996), no. 1, 135–139. MR 1392669
- A. Stipsicz, On the number of vanishing cycles in Lefschetz fibrations, Math. Res. Letters, to appear.
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
- MR Author ID: 346634
- Email: stipsicz@cs.elte.hu, astipsic@math.uci.edu
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1499-1502
- MSC (2000): Primary 53C27
- DOI: https://doi.org/10.1090/S0002-9939-00-05681-1
- MathSciNet review: 1712877