Virtual Betti numbers and virtual symplecticity of 4-dimensional mapping tori-大连理工大学数学科学学院(新)
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Virtual Betti numbers and virtual symplecticity of 4-dimensional mapping tori

2018-07-18
 

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.