Mathematical Sciences Geometry/Topology Seminar

November 2:
Speaker: Ronnie Lee (Yale)
Title: Intersection forms of even 4-manifolds

Abstract: In this talk, I will outline my joint work with Tian-Jun Li on the 10/8-conjecture. I.e. when a 4-manifold M has even intersection form $A = a E_8 \oplus b H$, then the number $b$ of the hyperbolic pairings is greater than or equal to the number $a$ of $E_8$. We proved this under the assumption that the 2-primary torsion part of $H_1(M,Z)$ is isomorphic to $Z_{2^i}$ for some i or $Z_2\oplus Z_2$, and Christian Bohr obtained a more general result in terms of the fundamental group of 4-manifold. I will explain some of these techniques as well as a number of intriquing conjectures on the fundamental groups and signatures of 4-manifolds.