Speaker: Yosuke Kubota (Shinshu Univ.)

Title: Band width and the Rosenberg index

Time/Date: 4:45-6:15pm, December 20 (Tue), 2022.

Room: Online (The Zoom link is the same as before. If you don't have one, please ask Kawahigashi.)

Abstract: Band width is a concept recently proposed by Gromov. It is based on the idea that when a certain band (i.e., manifold with two boundaries) is openly immersed to a target manifold M with positive scalar curvature metric, then its width is bounded by a uniform constant called the band width of M. A qualitative consequence is that infiniteness of the band width of M obstructs to positive scalar curvature. In this talk, infiniteness of a version of the band width, Zeidler's KO-band width, is dominated as a PSC obstruction by an existing obstruction, the Rosenberg index. This answers to a conjecture by Zeidler.