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.
STIPSICZ, ANDRAS I. (2001) "Sections of Lefschetz fibrations and Stein fillings," Turkish Journal of Mathematics: Vol. 25: No. 1, Article 5. Available at: https://journals.tubitak.gov.tr/math/vol25/iss1/5