Noncommutative Geometry and Topology in Prague

Mean cohomological independence dimension and radius of comparison

The concept of mean dimension for topological dynamics was developed by Lindenstrauss and Weiss, based on ideas of Gromov. Independently, and for different reasons entirely, Toms introduced the concept of radius of comparison for C*-algebras. It appears, however, that there is a connection between those two notions: to each topological dynamical system one can associate a C*-algebra (known as the crossed product or the transformation group C*-algebra), and there appears to be a connection between the mean dimension of the dynamical system and the radius of comparison of the associated C*-algebra. I will explain those concepts and a related concept which we call mean cohomological independence dimension, and discuss what is known about the connection between them. I don’t expect to prove anything in the talk.

This is joint work with N. Christopher Phillips.