## 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