Clustering of critical points in Lefschetz fibrations and the symplectic Szpiro inequality

Details Clustering of critical points in Lefschetz fibrations and the symplectic Szpiro inequality Clustering of critical points in Lefschetz fibrations and the symplectic Szpiro inequality

2002-04-11

arxiv.org/abs/math/0204153v2

Trans. Amer. Math. Soc. 355 (2003), 3217-3226.

Mathematics

Symplectic Geometry

minor corrections; to appear in Trans. Amer. Math. Soc

Scientific paper

10.1090/S0002-9947-03-03290-2

We prove upper bounds for the number of critical points in semistable
symplectic Lefschetz fibrations. We also obtain a new lower bound for the
number of nonseparting vanishing cycles in Lefschetz pencils, and reprove the
known lower bounds for the commutator lengths of Dehn twists.

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