Sections of Lefschetz fibrations and Stein fillings

Authors: ANDRAS I. STIPSICZ

Abstract: Using Eliashberg's theorem about Stein fillings of S^3 we prove that a section of a Lefschetz fibration over S^2 has nonnegative square. This observation, in particular, implies that the identity element 1\in \Gamma _g ^1 in the mapping class group of a genus-g surface with one boundary component cannot be written as a product of positive Dehn twists.

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