2020/09/28 by Hirshberg, Ilan, Phillips, N. Christopher
#37B05 #46L05 #46L55 #46L80 (secondary) #54H20 (primary) #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2009.13045
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 ZG (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.