İstanbul University Mathematics Department Seminars

Symplectic 4-Manifolds on the Noether Line and between the Noether and Half Noether Lines
Sümeyra Sakallı
Max Planck Institute for Mathematics, Bonn, Germany
Özet : It is known that all minimal complex surfaces of general type have exactly one (Seiberg-Witten) basic class, up to sign. Thus, it is natural to ask if one can construct smooth 4-manifolds with one basic class. First, Fintushel and Stern built simply connected, spin, smooth, nonsymplectic 4-manifolds with one basic class. Next, Fintushel, Park and Stern constructed simply connected, noncomplex, symplectic 4-manifolds with one basic class. Later Akhmedov constructed infinitely many simply connected, nonsymplectic and pairwise nondiffeomorphic 4-manifolds with nontrivial Seiberg-Witten invariants. Park and Yun also gave a construction of simply connected, nonspin, smooth, nonsymplectic 4-manifolds with one basic class. All these manifolds were obtained via knot surgeries, blow-ups and rational blow-downs. In this talk, we will first review some main concepts and recent techniques in symplectic 4-manifolds theory. Then we will construct minimal, simply connected and symplectic 4-manifolds on the Noether line and between the Noether and half Noether lines by the so-called star surgeries, and by using complex singularities. We will show that our manifolds have exotic smooth structures and each of them has one basic class. We will also present a completely geometric way of constructing certain configurations of Kodaira’s singularities in the rational elliptic surfaces, without using any monodromy arguments.
  Tarih : 06.11.2019
  Saat : 15:00
  Yer : Matematik Bölümü Bilgisayar Laboratuvarı
  Dil : English