Talk by Yajit Jain (Dept. of Mathematics, Northwestern University)

02/08/2021  4:10-5:15pm Zoom Talk

Abstract:  We will discuss the Rigidity Conjecture of Goette and Igusa, which states that, after stabilizing and then rationalizing, there are no exotic smoothings of manifold bundles with closed even dimensional fibers. After motivating this work through classical results such as Smale's h-cobordism theorem, and later work such as that of Dwyer, Weiss, and Williams, we will discuss fiberwise Poincare–Hopf theory and the duality theorems that lead to a proof of the aforementioned conjecture.