  We introduce a notion of mean cohomological independence dimension for
actions of discrete amenable groups on compact metrizable spaces, as a variant
of mean dimension, and use it to obtain lower bounds for the radius of
comparison of the associated crossed product C*-algebras. Our general theory
gives the following for the minimal subshifts constructed by Dou in 2017. Let G
be a countable amenable group, let Z be a polyhedron, and let T be Dou's
subshift of Z^G (which also depends on a density parameter). Then the radius of
comparison of the crossed product is greater than r (1/2) mdim (T) - 2, in
which r depends on the density parameter and is close to 1 when the density
parameter is close to 1. If Z is even dimensional and has nonvanishing rational
cohomology in degree dim (Z), then the radius of comparison of the crossed
product is greater than (1/2) mdim (T) - 1, regardless of what the density
parameter is.

Operator Algebras;Dynamical Systems