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Topology/Geometry Seminar

Topological rigidity of the first Betti number and Ricci flow smoothing

Shaosai Huang (University of Wisconsin Madison)

Location:  zoom link: https://rutgers.zoom.us/j/96839448491?pwd=NHNWcVFKTWpkRDZWcVVhVm9mYTNGUT09
Date & time: Tuesday, 20 October 2020 at 3:50PM - 4:50PM

The infranil fiber bundle is a typical structure appeared in the collapsing geometry with bounded sectional curvature. In this talk, I will discuss a topological condition on the first Betti numbers that guarantees a torus fiber bundle structure (a special type of infranil fiber bundle) for collapsing manifolds with only Ricci curvature bounded below. The main technique applied here is smoothing by Ricci flows. This covers my joint with Bing Wang.