Topological Rigidity of the Dynamic Asymptotic Dimension

Samantha Pilgrim (University of Glasgow)

Thursday 24th October 16:00-17:00 Maths 311B

Abstract

The Dynamic Asymptotic Dimension (DAD) of a group action introduced by Guentner, Willett, and Yu measures the large-scale complexity of the orbits in a similar way to Gromov's asymptotic dimension.  Although known to be related to dimension theories for group actions which are sensitive to the topology of the space being acted on, it has been conjectured for some time that the DAD coincides with the asymptotic dimension of the acting group whenever the DAD is finite.  This talk will present the main ideas behind the proof of this conjecture for all free actions by countable groups on finite-dimensional compact metric spaces.  In particular, the methods involve a new application of the inductive dimension from topology.  

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