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.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:Using Eliashberg's theorem about Stein fillings of S3 we prove that a section of a Lefschetz fibration over S2 has nonnegative square.
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Key Findings & Data:Using Eliashberg's theorem about Stein fillings of S3 we prove that a section of a Lefschetz fibration over S2 has nonnegative square.
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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Turk. J. Math. · (2001) · 97-102. Full text: pdf Other articles published in the same issue: Turk. J. Math.
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.
STIPSICZ, A. I. (2022). Sections of Lefschetz fibrations and Stein fillings. Turkish Journal of Mathematics, Cilt: 25 - Sayı: 1, 97–101. https://ajindex.com/articles/608887