October 20, 2021
The global shape of universal covers- Virtual Talk — On Zoom
If one starts with the universal cover of a compact space, and looks at it from very far, what would the limiting shape be? It is well known (Gromov-Pansu Theorem) that if there is a limiting shape, then it must be a Carnot-Carathéodory group; a simply connected nilpotent Lie group with a special type of invariant metric.
I will talk about the similar problem of studying the limit shapes of universal covers of sequences of spaces shrinking to a point.