Journals / Turkish Journal of Mathematics / 2001 / Cilt: 25 - Sayı: 1
Sections of Lefschetz fibrations and Stein fillings
- Pages
- 97–101
- DOI
- —
Abstract
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.
Özet
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.