Radius of comparison and mean cohomological independence dimension

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. For any countable amenable group G and any polyhedron Z, Dou's subshift T of Z^G with density parameter ρ satisfies [Formula presented] If k=dim⁡(Z) is even and Hˇ^k(Z;Q)≠0, then [Formula presented] regardless of what ρ is.