Warped cones as a bridge between dynamics and coarse geometry

04.05.2021 15:00 - 17:00

Damian Sawicki (KU Leuven)

I will discuss the warped cone construction, which was introduced by J. Roe in 2005 and is currently enjoying a renaissance. The warped cone is an unbounded metric space associated to an action of a finitely generated group on a compact space, like the sphere or the Cantor set. I will explain how this construction can be used in both dynamics and coarse geometry. On the one hand, for actions with spectral gaps, the construction yields super-expander graphs and counterexamples to the coarse Baum–Connes conjecture. On the other hand, it can be used to obtain upper bounds on notions of dimension of group actions, like dynamic asymptotic dimension, which are of key importance in the study of crossed product C*-algebras associated to group actions.



G. Arzhantseva, A. Evetts
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