İstanbul University Mathematics Department Seminars

Geography of Lefschetz Fibrations over S^2
Adalet Çengel
Boğaziçi University, Turkey
Özet : Donaldson and Gompf have shown that Lefschetz fibrations and symplectic 4-manifolds are very close to each other. A Lefschetz fibration is a fibration of a smooth 4-manifold over a surface with some singular fibers. The general fiber of this fibration is another orientable surface. The isomorphism class of a Lefschetz fibration is characterized by its monodromy representation. This gives a remarkable connection between symplectic 4-manifolds and mapping class groups of surfaces. In this talk, I will first define genus-g Lefschetz fibrations over S^2 and their monodromies. Then I introduce the Euler characteristic and the signature of a Lefschetz fibration. After giving computations of them, I describe the geography problem. In the end, I will conclude with the updated results.
  Tarih : 28.11.2018
  Saat : 14:00
  Yer : İ.Ü. Matematik Bölümü D-II
  Dil : Turkish