Indecomposability of certain Lefschetz fibrations

Stipsicz, András

doi:10.1090/S0002-9939-00-05681-1

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.