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

Braungardt, V.; Kotschick, D.

doi:10.1090/S0002-9947-03-03290-2

Clustering of critical points in Lefschetz fibrations and the symplectic Szpiro inequality
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by V. Braungardt and D. Kotschick PDF

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

Abstract:

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

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