Let G be a countable amenable group and X be a subshift over G. We show that the set of topological entropies of symbolic factors of X is dense in the interval [0, h(X)]. There were known results for the case of Z-topological dynamics by Shub-Weiss and Lindenstrauss. Our development uses a general marker lemma for amenable groups, and quasi-tilings of the group to estimate the entropies of factors of X defined by clopen sets generated by marker lemma. We also present relativized version of the result. This is a joint work with Ronnie Pavlov and Kevin McGoff.

 

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