Using Eliashberg's theorem about Stein fillings of S3 we prove that a section of a Lefschetz fibration over S2 has nonnegative square. This observation, in particular, implies that the identity element 1\in G 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.

Using Eliashberg's theorem about Stein fillings of S3 we prove that a section of a Lefschetz fibration over S2 has nonnegative square. This observation, in particular, implies that the identity element 1\in G 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.