Academic Report
Title: Virtual Betti numbers and virtual symplecticity of 4-dimensional mapping tori
Reporter: Prof. Tian-Jun Li (University of Minnesota)
Time: July 30, 2018 (Monday) PM 15:30-16:30
Location: A1101# room, Innovation Park Building
Contact: Prof. LEI Fengchun(tel: 84706472)
Abstract: We compute the virtual first Betti numbers of 4-manifolds fibering over S^1 with prime 3-manifold fiber. As an application, we show that if such a manifold is symplectic with nonpositive Kodaira dimension, then the fiber itself is a sphere or torus bundle over S^1. In a different direction, we prove that if the 3-dimensional fiber of such a 4-manifold is virtually fibered then the 4-manifold is virtually symplectic unless its virtual first Betti number is 1. This is a joint work with Yi Ni.
The brief introduction to the reporter: Tian-Jun Li, Professor, Associate Head at School of Mathematics, University of Minnesota. BS, Beijing University; PhD, Brandeis University; Postdoc, Yale University, Institute for Advanced Study; Assistant Professor, Princeton University. Research interests: four manifold theory and symplectic geometry. Main contributions: Seiberg-Witten theory of smooth 4-manifolds with b+=1, Classifications of symplectic rational and ruled 4-manifolds and symplectic and Lagrangian surfaces, topology of symplectic Calabi-Yau surfaces, minimal genus problem, symplectic birational geometry in higher dimension.
